❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦❢✐❛✱ ❈✐ê♥❝✐❛s ❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦ Pr❡t♦
Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❆♣❧✐❝❛❞❛ à ▼❡❞✐❝✐♥❛ ❡ ❇✐♦❧♦❣✐❛
❩❡r♦s ❞❡ ❋✐s❤❡r ❡ ❛s♣❡❝t♦s ❝rít✐❝♦s ❞♦ ♠♦❞❡❧♦
❞❡ ■s✐♥❣ ❞✐♣♦❧❛r
❏❛❝②❛♥❛ ❙❛r❛✐✈❛ ▼❛rt❤❡s ❋♦♥s❡❝❛
❏❆❈❨❆◆❆ ❙❆❘❆■❱❆ ▼❆❘❚❍❊❙ ❋❖◆❙❊❈❆
❩❡r♦s ❞❡ ❋✐s❤❡r ❡ ❛s♣❡❝t♦s ❝rít✐❝♦s ❞♦ ♠♦❞❡❧♦ ❞❡
■s✐♥❣ ❞✐♣♦❧❛r
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡
❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛s ❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦
Pr❡t♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠♦
♣❛rt❡ ❞❛s ❡①✐❣ê♥❝✐❛s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦
tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿
❋ís✐❝❛ ❆♣❧✐❝❛❞❛ à ▼❡❞✐❝✐♥❛ ❡ ❇✐♦❧♦❣✐❛
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ◆❡❧s♦♥ ❆✉❣✉st♦ ❆❧✈❡s
❆❯❚❖❘■❩❖ ❆ ❘❊P❘❖❉❯➬➹❖ ❊ ❉■❱❯▲●❆➬➹❖ ❚❖❚❆▲ ❖❯ P❆❘❈■❆▲ ❉❊❙❚❊ ❚❘❆❇❆▲❍❖✱ P❖❘ ◗❯❆▲◗❯❊❘ ▼❊■❖ ❈❖◆❱❊◆❈■❖◆❆▲ ❖❯ ❊▲❊❚❘Ô◆■❈❖✱ P❆❘❆ ❋■◆❙ ❉❊ ❊❙❚❯❉❖ ❊ P❊❙◗❯■❙❆✱ ❉❊❙❉❊ ◗❯❊ ❈■❚❆❉❆ ❆ ❋❖◆❚❊✳
❋♦♥s❡❝❛✱ ❏❛❝②❛♥❛ ❙❛r❛✐✈❛ ▼❛rt❤❡s✳
❩❡r♦s ❞❡ ❋✐s❤❡r ❡ ❛s♣❡❝t♦s ❝rít✐❝♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❞✐♣♦❧❛r✴
❏❛❝②❛♥❛ ❙❛r❛✐✈❛ ▼❛rt❤❡s ❋♦♥s❡❝❛❀ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ❉r✳ ◆❡❧s♦♥
❆✉❣✉st♦ ❆❧✈❡s✳ ❘✐❜❡✐rã♦ Pr❡t♦✱ ✷✵✶✶✳ ✶✷✼ ♣✳
❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦ ✲ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❆♣❧✐❝❛❞❛ à ▼❡❞✐❝✐♥❛ ❡ ❇✐♦❧♦❣✐❛✮ ✲ ❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛s
❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦ Pr❡t♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳
◆♦♠❡✿ ❋♦♥s❡❝❛✱ ❏❛❝②❛♥❛ ❙❛r❛✐✈❛ ▼❛rt❤❡s
❚ít✉❧♦✿ ❩❡r♦s ❞❡ ❋✐s❤❡r ❡ ❛s♣❡❝t♦s ❝rít✐❝♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❞✐♣♦❧❛r
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛s ❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦ Pr❡t♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠♦ ♣❛rt❡ ❞❛s ❡①✐❣ê♥❝✐❛s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s
❆♣r♦✈❛❞♦ ❡♠✿ ✴ ✴ ✳
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛
Pr♦❢✳ ❉r✳ ✿ ■♥st✐t✉✐çã♦✿
❏✉❧❣❛♠❡♥t♦✿ ❆ss✐♥❛t✉r❛✿
Pr♦❢✳ ❉r✳ ✿ ■♥st✐t✉✐çã♦✿
❏✉❧❣❛♠❡♥t♦✿ ❆ss✐♥❛t✉r❛✿
Pr♦❢✳ ❉r✳ ✿ ■♥st✐t✉✐çã♦✿
✐✈
❆❣r❛❞❡❝✐♠❡♥t♦s
●♦st❛r✐❛ ♥❡st❡ ❛❣r❛❞❡❝✐♠❡♥t♦ ❞❡ ❧❡♠❜r❛r ❞❛s ♣❡ss♦❛s q✉❡ ❝♦♥tr✐❜✉✐r❛♠ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ ❡♠ ♣r✐♠❡✐r♦ ❧✉❣❛r ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ◆❡❧s♦♥✱ ♣❡❧❛ ✐❞❡❛❧✐③❛çã♦ ❞♦ ♣r♦❥❡t♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ♣♦r t❡r ♠❡ r❡❝❡❜✐❞♦ ❞❡ ❜r❛ç♦s ❛❜❡rt♦s ❝♦♠♦ s✉❛ ♦r✐❡♥t❛♥❞❛✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦ q✉❡ t❡♠ ❛♦ s❡✉ tr❛❜❛❧❤♦ ❡ ❛♦s s❡✉s ❛❧✉♥♦s✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♠♣r❡❡♥sã♦ q✉❡ t❡✈❡ ❝♦♠✐❣♦ ❞✐❛♥t❡ ❞♦s ♣r♦❜❧❡♠❛s q✉❡ ✈❡♥❤♦ ❡♥❢r❡♥t❛♥❞♦ ♥❡st❡s ú❧t✐♠♦s ❛♥♦s✳ ❆❣r❛❞❡ç♦ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞♦ ■❜✐❧❝❡✲❯◆❊❙P✱ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ✐♥t❡r❞✐s❝✐♣❧✐♥❛r ❡ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡♠ s❡❣✉✐r ❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦✉t♦r❡s ❏♦r❣❡ ❈❤❛❤✐♥❡✱ q✉❡ ❞❡s♣❡rt♦✉ ❡♠ ♠✐♠ ♦ ✐♥t❡r❡ss❡ ♣❡❧❛s s✐♠✉❧❛çõ❡s ❡♠ ❢ís✐❝❛ ❡st❛tíst✐❝❛✱ ❏♦sé ❘♦❜❡rt♦ ❘✉❣❣✐❡r♦✱ ♣❡❧❛s ❛✉❧❛s ❞❡ ❢ís✐❝❛ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ t❛♠❜é♠ ♣❡❧❛ s✉❛ ❝♦♦r❞❡♥❛çã♦ ♥♦ ❝✉rs♦ ❞❡ ❋ís✐❝❛ ❇✐♦❧ó❣✐❝❛✱ ❊❧s♦ ❉r✐❣♦ ❋✐❧❤♦✱ ♣❡❧❛s ❛❣r❛❞á✈❡✐s ❛✉❧❛s ❞❡ ❢ís✐❝❛ ♠❛t❡♠át✐❝❛ ❡ q✉â♥t✐❝❛✱ ♣❡❧❛s ♦r✐❡♥t❛çõ❡s✱ ❝❛r✐♥❤♦ ❡ ❛♠✐③❛❞❡✱ ❡ ▼❛r❝❡❧♦ ❋♦ss❡②✱ ♣❡❧♦s q✉❛s❡ três ❛♥♦s ❞❡ tr❛❜❛❧❤♦ ❥✉♥t♦s ❡ ♣❡❧❛ ❛♠✐③❛❞❡✳ ❆❣r❛❞❡ç♦ ❛ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ♣r♦❣r❛♠❛ ❋❆▼❇✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦✉t♦r❡s ❆❧❡①❛♥❞r❡✱ ❣r❛♥❞❡ ❝♦♥s❡❧❤❡✐r♦✱ ❡ ▼❛r❝❡❧♦ ▼✉❧❛t♦✱ ♣❡❧❛ ót✐♠❛ ❝♦♦r❞❡♥❛çã♦✳ ❆♦s ♣r♦❢s✳ ❉rs✳ ▼❛r❝♦ ❆♥tô♥✐♦ ❞❛ ❙✐❧✈❛ ❡ ❆♥tô♥✐♦ ❈❛❧✐r✐✱ ❞❛ ❋❈❋❘P✳ ❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ◆✐❧③❛✱ ❙ô♥✐❛✱ ❘✐❝❛r❞♦✱ ❋á❜✐♦✱ ❞❡♥tr❡ ♦✉tr♦s ❡ ❛♦ ♣❡ss♦❛❧ ❞❛ s❡çã♦ ❞❡ ♣ós✱ ❡♠ ❡s♣❡❝✐❛❧ ▼❛r✐❛ ■♥ês ❡ ❉❡♥✐s❡✳ ❆❣r❛❞❡ç♦ ❝♦♠ ❝❛r✐♥❤♦ ❛♦s ♠❡✉s ❝♦❧❡❣❛s ❞❡ ❧❛❜♦r❛tór✐♦✱ q✉❡ ❛❝❛❜❛r❛♠ ♣♦r s❡ t♦r♥❛r ❣r❛♥❞❡s ❛♠✐❣♦s✿ ▲❡❛♥❞r♦✱ ❣r❛♥❞❡ ❝♦❧❛❜♦r❛❞♦r ❞❡ss❡ tr❛❜❛❧❤♦✱ ♣❡❧❛ ❛❥✉❞❛ ❡ ❛♠✐③❛❞❡✱ ❘❛❢❛❡❧ ✭s❛✉❞❛❞❡s✮ ♣❡❧❛s ❝❡r✈❡❥❛❞❛s ❡ ❝♦♥✈❡rs❛s ❞❡ ❢ís✐❝♦✱ ▼❛t❤❡✉s✱ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❡♠ ♠❡ ♦✉✈✐r t❛❣❛r❡❧❛r ♥❛s ❤♦r❛s ❞❡ ❛❧♠♦ç♦ ❡ ❧❛♥❝❤❡ s❡♠ r❡❝❧❛♠❛r ❡ ●✉✐❞♦❧✐♥✱ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ♥♦ss❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❞✐❛♥t❡ ❞♦s ♣r♦❜❧❡♠❛s ❞♦ ❆t❧❛s✳ ❆♦ ♠❡✉ ♥❛♠♦r❛❞♦ ❋r❛♥❝✐s❝♦✱ ♣❡❧♦ ❛♠♦r✱ ♣❛❝✐ê♥❝✐❛ ❡ r❡s✐stê♥❝✐❛ ❞✐❛♥t❡ ❞❡ ♠❡✉s
✈✐✐
❋♦✐ ♦ t❡♠♣♦ q✉❡ ❞❡❞✐❝❛st❡s à t✉❛ r♦s❛ q✉❡ ❢❡③ t✉❛ r♦s❛ tã♦ ✐♠♣♦rt❛♥t❡
❘❡s✉♠♦
❋❖◆❙❊❈❆✱ ❏✳ ❙✳ ▼✳ ❩❡r♦s ❞❡ ❋✐s❤❡r ❡ ❛s♣❡❝t♦s ❝rít✐❝♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❞✐♣♦❧❛r✳ ✶✷✼ ♣✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦✮ ✲ ❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛s ❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦ Pr❡t♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❘✐❜❡✐rã♦ Pr❡t♦✱ ✷✵✶✶✳
❊st✉❞❛♠♦s ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❝rít✐❝♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❝♦♠ ✐♥t❡r❛çã♦ ❞✐♣♦❧❛r✱ ❡♠ r❡❞❡s ❜✐❞✐♠❡♥s✐♦♥❛✐s r❡❣✉❧❛r❡s✳ ❊st❡ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛ ✉♠ ❝❡♥ár✐♦ ❢❡♥♦♠❡♥♦❧♦❣✐❝❛♠❡♥t❡ r✐❝♦ ❞❡✈✐❞♦ ❛♦ ❡❢❡✐t♦ ❞❡ ❢r✉str❛çã♦ ❝❛✉s❛❞♦ ♣❡❧❛ ❝♦♠♣❡t✐çã♦ ❡♥tr❡ ❛s ✐♥t❡r❛çõ❡s ❞❡ tr♦❝❛ ❞♦ ■s✐♥❣ ♣✉r♦ ❡ ❛ ✐♥t❡r❛çã♦ ❞✐♣♦❧❛r✳ ❆ ❝r✐t✐❝❛❧✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❢♦✐ ❡st✉❞❛❞❛ ❛ ♣❛rt✐r ❞❛s r❡❧❛çõ❡s ❞❡ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ❊st❛ ❛❜♦r❞❛❣❡♠ ♥✉♥❝❛ ❢♦✐ ✉t✐❧✐③❛❞❛ ♥♦ ❡st✉❞♦ ❞♦ ♠♦❞❡❧♦ ❡♠ q✉❡stã♦✳ ◆♦ss♦ ❡st✉❞♦ s❡ ❜❛s❡✐❛ ❡♠ s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✉s❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ♠✉❧t✐❝❛♥ô♥✐❝♦✳ ❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ♦❜t❡r ❛ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛ ❡♠ ❢✉♥çã♦ ❞♦ ❛❝♦♣❧❛♠❡♥t♦ δ ✭r❛③ã♦ ❡♥tr❡ ❛s ✐♥t❡♥s✐❞❛❞❡s
❞♦s ❛❝♦♣❧❛♠❡♥t♦s ❢❡rr♦♠❛❣♥ét✐❝♦ ❡ ❞✐♣♦❧❛r✮ ❡ ❝♦♥str✉✐r ✉♠❛ ♣❛rt❡ ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❞♦ ♠♦❞❡❧♦✳ ❉✐❢❡r❡♥t❡s ♣❛rt❡s ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❛✐♥❞❛ ♥ã♦ ❛♣r❡s❡♥t❛♠ ✐♥❞✐❝❛çõ❡s ❝♦♥❝❧✉s✐✈❛s ❛ r❡s♣❡✐t♦ ❞❛ ♦r❞❡♠ ❞❛s ❧✐♥❤❛s ❞❡ tr❛♥s✐çã♦✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❤á ❡✈✐❞ê♥❝✐❛s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ✉♠ ♣♦♥t♦ tr✐❝rít✐❝♦ ♣❛r❛ δ ♥♦ ✐♥t❡r✈❛❧♦ [0.90,1.00]✱
♠❛s s✉❛ ❧♦❝❛❧✐③❛çã♦ ♣r❡❝✐s❛ ♥ã♦ é ❝♦♥❤❡❝✐❞❛✳ ◆♦ss❛s s✐♠✉❧❛çõ❡s ✐♥❞✐❝❛♠ q✉❡ ♦ ♣♦♥t♦ tr✐❝rít✐❝♦ ♥ã♦ s❡ ❧♦❝❛❧✐③❛ ♥♦ ✐♥t❡r✈❛❧♦ ❛❝✐♠❛✳ ◆♦ss♦s r❡s✉❧t❛❞♦s ♠♦str❛r❛♠ q✉❡✱ ♣❛r❛
δ∈[0.89,1.10]✱ ❛ ❢❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s ❝♦♠h= 1 ♣❛ss❛ ♣❛r❛ ❛ ❢❛s❡ t❡tr❛❣♦♥❛❧ ❛tr❛✈és
❞❡ ✉♠❛ tr❛♥s✐çã♦ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✳ ❆ ❛♥á❧✐s❡ ❞❡ ❋❙❙ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ♥❛ ✈❛r✐á✈❡❧ t❡♠♣❡r❛t✉r❛✱ ❛♣r❡s❡♥t❛✱ ♣❛r❛ δ = 1.20✱ ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡
❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ ❡ ♣❛r❛δ= 1.30✱ ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❉❡ss❛
❢♦r♠❛✱ ♦ ♣♦♥t♦ tr✐❝rít✐❝♦ ♦❝♦rr❡ s♦♠❡♥t❡ ❡♥tr❡δ= 1.20❡1.30✳ ❘❡❛❧✐③❛♠♦s ✉♠ ❡st✉❞♦
✐① ❝♦♠♣❧❡♠❡♥t❛r ❜❛s❡❛❞♦ ♥❛ ❛❜♦r❞❛❣❡♠ ♠✐❝r♦❝❛♥ô♥✐❝❛ ❡ ♦❜s❡r✈❛♠♦s ❞✉❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ ♣❛r❛δ= 1.20❡ ❞✉❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠
❆❜str❛❝t
❋❖◆❙❊❈❆✱ ❏✳ ❙✳ ▼✳ ❋✐s❤❡r✬s ③❡r♦s ❛♥❞ ❝r✐t✐❝❛❧ ❛s♣❡❝ts ♦❢ t❤❡ ❞✐♣♦❧❛r ■s✐♥❣ ♠♦❞❡❧✳ ✶✷✼ ♣✳ ❉✐ss❡rt❛t✐♦♥ ✭▼✳❙❝✳✮ ✲ ❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛s ❡ ▲❡tr❛s ❞❡ ❘✐❜❡✐rã♦ Pr❡t♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❘✐❜❡✐rã♦ Pr❡t♦✱ ✷✵✶✶✳
❲❡ st✉❞② t❤❡ ❝r✐t✐❝❛❧ ❜❡❤❛✈✐♦r ♦❢ t❤❡ ❞✐♣♦❧❛r ■s✐♥❣ ♠♦❞❡❧ ♦♥ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ r❡❣✉❧❛r ❧❛tt✐❝❡s✳ ❚❤✐s ♠♦❞❡❧ ♣r❡s❡♥ts ❛ ♣❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧❧② r✐❝❤ s❝❡♥❛r✐♦ ❞✉❡ t♦ t❤❡ ❡✛❡❝t ♦❢ ❢r✉str❛t✐♦♥ ❝❛✉s❡❞ ❜② t❤❡ ❝♦♠♣❡t✐t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ♣✉r❡ ■s✐♥❣ ✐♥t❡r❛❝t✐♦♥ ❛♥❞ t❤❡ ❞✐♣♦❧❛r ♦♥❡✳ ❚♦ st✉❞② t❤❡ ❝r✐t✐❝❛❧✐t② ♦❢ t❤✐s ♠♦❞❡❧ ✇❡ ❛♣♣❧② ✜♥✐t❡ s✐③❡ s❝❛❧✐♥❣ r❡❧❛t✐♦♥s ❢♦r t❤❡ ♣❛rt✐t✐♦♥ ❢✉♥❝t✐♦♥ ③❡r♦s ✐♥ t❤❡ ❝♦♠♣❧❡① t❡♠♣❡r❛t✉r❡ ♣❧❛♥❡✳ ❚❤❡ ♣❛rt✐t✐♦♥ ❢✉♥❝t✐♦♥ ③❡r♦s ❛♥❛❧②s✐s ❤❛s ♥❡✈❡r ❜❡❡♥ ✉s❡❞ ❜❡❢♦r❡ t♦ st✉❞② s✉❝❤ ♠♦❞❡❧ ✇✐t❤ ❧♦♥❣✲r❛♥❣❡ ✐♥t❡r❛❝t✐♦♥s✳ ❖✉r st✉❞② r❡❧✐❡s ♦♥ ▼♦♥t❡ ❈❛r❧♦ s✐♠✉❧❛t✐♦♥s ✉s✐♥❣ t❤❡ ♠✉❧t✐❝❛♥♦♥✐❝❛❧ ❛❧❣♦r✐t❤♠✳ ❖✉r ❣♦❛❧ ✐s t♦ ♦❜t❛✐♥ t❤❡ ❝r✐t✐❝❛❧ t❡♠♣❡r❛t✉r❡ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ❝♦✉♣❧✐♥❣ δ ✭t❤❡ r❛t✐♦ ❜❡t✇❡❡♥ t❤❡ ❢❡rr♦♠❛❣♥❡t✐❝ ❛♥❞ ❞✐♣♦❧❛r
❝♦✉♣❧✐♥❣s✮ t♦ ❝♦♥str✉❝t ❛ ♣❛rt ♦❢ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠✳ ❉✐✛❡r❡♥t ♣❛rts ♦❢ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ❞♦ ♥♦t ♣r❡s❡♥t ❛ ❝♦♥❝❧✉s✐✈❡ r❡s✉❧ts ❛❜♦✉t t❤❡ ♦r❞❡r ♦❢ t❤❡ ♣❤❛s❡ tr❛♥s✐t✐♦♥ ❧✐♥❡s✳ ■♥ ♣❛rt✐❝✉❧❛r✱ t❤❡r❡ ✐s ❡✈✐❞❡♥❝❡ ♦❢ ❛ tr✐❝r✐t✐❝❛❧ ♣♦✐♥t ❢♦r δ ∈ [0.90,1.00]✱ ❜✉t
✐ts ♣r❡❝✐s❡ ❧♦❝❛t✐♦♥ ✐s ✉♥❦♥♦✇♥✳ ❖✉r s✐♠✉❧❛t✐♦♥s ✐♥❞✐❝❛t❡ t❤❛t t❤❡ tr✐❝r✐t✐❝❛❧ ♣♦✐♥t ✐s ♥♦t ❧♦❝❛t❡❞ ✐♥ t❤❡ ❛❜♦✈❡ r❛♥❣❡✳ ❖✉r ❋❙❙ ❛♥❛❧②s✐s s❤♦✇ t❤❛t ❢♦r δ = 1.20 t❤❡
str✐♣❡❞✲t❡tr❛❣♦♥❛❧ tr❛♥s✐t✐♦♥ ✐s ❛ s❡❝♦♥❞✲♦r❞❡r ♣❤❛s❡ tr❛♥s✐t✐♦♥ ❛♥❞ ❢♦rδ = 1.30✐t ✐s
❛ ✜rst✲♦r❞❡r ♦♥❡✳ ❚❤✉s✱ t❤❡ tr✐❝r✐t✐❝❛❧ ♣♦✐♥t ♠✉st ♦❝❝✉r ❜❡t✇❡❡♥δ= 1.2❛♥❞δ= 1.3✳
❲❡ ❤❛✈❡ ✉s❡❞ ❛ ♠✐❝r♦❝❛♥♦♥✐❝❛❧ ❛♣♣r♦❛❝❤ t♦ st✉❞② t❤❡ ❝r✐t✐❝❛❧✐t② ♦❢ t❤✐s ♠♦❞❡❧ t♦♦✳ ❚❤✐s ❛♣♣r♦❛❝❤ ✐♥❞✐❝❛t❡s t✇♦ s❡❝♦♥❞✲♦r❞❡r ♣❤❛s❡ tr❛♥s✐t✐♦♥s ❢♦r δ = 1.20 ❛♥❞ t✇♦
✜rst✲♦r❞❡r ♣❤❛s❡ tr❛♥s✐t✐♦♥s ❢♦r δ = 1.30✳ ❚❤❡r❡❢♦r❡✱ ✐t ♣r❡s❡♥ts ❡✈✐❞❡♥❝❡s ❢♦r t❤❡
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❋❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s ❝♦♠ ❧❛r❣✉r❛ h= 4✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✶✳✷ ❉✐❢❡r❡♥t❡s ❢❛s❡s ♦❜s❡r✈❛❞❛s ❡♠ ✜❧♠❡s ✜♥♦s ❞❡ ❋❡ ❡♠ ❈✉ ♣❡❧❛ té❝♥✐❝❛ ❙❊▼P❆ ✭♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛ ❝♦♠ ❛♥á❧✐s❡ ❞❡ ♣♦▲❛r✐③❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✸ ❈♦♥✜❣✉r❛çõ❡s ❞♦s s♣✐♥s ♣❛r❛ ✉♠❛ r❡❞❡ ❞❡ ❧❛r❣✉r❛L= 56♦❜t✐❞❛s ♣♦r
s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✶✳✹ ❍✐st♦❣r❛♠❛s ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ es ♦❜t✐❞♦s ❞❡ ✉♠❛ s✐♠✉❧❛çã♦
♠✉❧t✐❝❛♥ô♥✐❝❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ❤✐st♦❣r❛♠❛s r❡♣❡s❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s ♥♦ ❡♥s❡♠❜❧❡ ❝❛♥ô♥✐❝♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ✉♠❛ r❡❞❡ 20×20✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✶ ✭❛✮ ❉✐❛❣r❛♠❛ P T ♣❛r❛ ✉♠ s✐st❡♠❛ ✢✉✐❞♦✳ ✭❜✮ ❉✐❛❣r❛♠❛ HT ♣❛r❛
✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦ s✐♠♣❧❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷ ✭❛✮ ❉✐❛❣r❛♠❛ ρT ♣❛r❛ ✉♠ s✐st❡♠❛ ✢✉✐❞♦ ♣✉r♦✳ ✭❜✮ ❉✐❛❣r❛♠❛ M T
♣❛r❛ ✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦ s✐♠♣❧❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✸ ▼❡❞✐❞❛s ❞❛ ❝✉r✈❛ ❞❡ ❝♦❡①✐stê♥❝✐❛ ♣❛r❛ ✢✉✐❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹ ■❧✉str❛çã♦ ❞❡ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ ❡s❝❛❧❛ ❞❡ ✉♠❛ ❢✉♥çã♦f(r) ♣❛r❛ ✉♠❛
❢✉♥çã♦ f(λr)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✷✳✺ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❝♦rr❡❧❛çã♦ ξ ♣❛r❛ ❞✐❢❡r❡♥t❡s
t❡♠♣❡r❛t✉r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
①✐✐✐ ✸✳✶ ❈♦♠♣♦rt❛♠❡♥t♦ ❛♥❛❧ít✐❝♦ ❛ ✉♠❛ ❞❛❞❛ t❡♠♣❡r❛t✉r❛ ❞❛s ❢✉♥çõ❡s
t❡r♠♦❞✐♥â♠✐❝❛s ♣❛r❛✿ ✭❛✮ ✉♠ s✐st❡♠❛ ❡♠ ✉♠❛ ú♥✐❝❛ ❢❛s❡✱ ✭❜✮ ✉♠ s✐st❡♠❛ q✉❡ ♣❛ss❛ ♣♦r ❞✉❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ■❧✉str❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ♣ró①✐♠♦s ❛♦
❡✐①♦ r❡❛❧ ♣♦s✐t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸ ■❧✉str❛çã♦ ❞❡ ✉♠ ♣❡q✉❡♥♦ ♣❡❞❛ç♦ ❞❛ r❡❞❡ ❞❡ s♣✐♥s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡
■s✐♥❣ ✶❉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✶ ❈♦♥✜❣✉r❛çõ❡s ❞❡ s♣✐♥ ♥❛s t❡♠♣❡r❛t✉r❛s ❞❡ tr❛♥s✐çã♦ ♣❛r❛ ✉♠❛ r❡❞❡
L= 56❡δ= 2✳ ✭❛✮ ❢❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s✱ ✭❜✮ s✐st❡♠❛ ♥❛ t❡♠♣❡r❛t✉r❛ ❞❡
tr❛♥s✐çã♦ ❞❛ ❢❛s❡ ❞❡ ❢❛✐①❛s ♣❛r❛ ❛ ❢❛s❡ ♥❡♠át✐❝❛✱ ✭❝✮ ❢❛s❡ ♥❡♠át✐❝❛✱ ✭❞✮ s✐st❡♠❛ ♥❛ t❡♠♣❡r❛t✉r❛ ❞❡ tr❛♥s✐çã♦ ❞❛ ❢❛s❡ ♥❡♠át✐❝❛ ♣❛r❛ ♦ ❧íq✉✐❞♦ t❡tr❛❣♦♥❛❧✱ ✭❡✮ ❧íq✉✐❞♦ t❡tr❛❣♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✭❛✮ ✉♠❛ ❞❡s❧♦❝❛çã♦✱ ✭❜✮ ❡ ✭❝✮ t✐♣♦s ❞❡
❞✐s❝❧✐♥❛çõ❡s q✉❡ ♣♦❞❡♠ ♦❝♦rr❡r ❡♠ ❢❛s❡s ❞♦ t✐♣♦ ❢❛✐①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✸ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❡♠ ❢✉♥çã♦ ❞♦ ❛❝♦♣❧❛♠❡♥t♦δ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣
❞✐♣♦❧❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✹ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❡♠ ❢✉♥çã♦ ❞♦ ❛❝♦♣❧❛♠❡♥t♦ δ ♦❜t✐❞♦ ♣♦r ❝á❧❝✉❧♦ ❞❡
❝❛♠♣♦ ♠é❞✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✻✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❝♦♥❞✐çõ❡s ♣❡r✐ó❞✐❝❛s ❞❡ ❝♦♥t♦r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✻✳✷ ❊♥❡r❣✐❛s ❝❛❧❝✉❧❛❞❛s ♣❛r❛ ♦s ❡st❛❞♦s ❞♦ t✐♣♦ ❢❛✐①❛s h = 1✱ 2 ❡ 3 ❡♠
❢✉♥çã♦ ❞❡ δ ♣❛r❛ L= 128✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✻✳✸ ❍✐st♦❣r❛♠❛s ❞❡ ❡♥❡r❣✐❛ ♣r♦❞✉③✐❞♦s ❡♠ ❞✐❢❡r❡♥t❡s r❡♣❡t✐çõ❡s n ♣❛r❛
❛t✉❛❧✐③❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦san(E)❡bn(E)♣❛r❛δ= 0.89✳ ✻✵
✻✳✹ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ L= 48✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
①✐✈ ✻✳✻ ❩❡r♦s ❡♠ u = e−β ♣❛r❛ L = 32 ♦❜t✐❞♦s ❞❡ ✉♠❛ ❞❛s ✶✻ sér✐❡s
♣r♦❞✉③✐❞❛s ♣❛r❛ ✭❛✮ ✭δ= 0.89✮ t♦❞♦s ♦s ③❡r♦s ♦❜t✐❞♦s✱ ✭❜✮ ✭δ = 0.89✮
❛♠♣❧✐❛çã♦ ❞❛ r❡❣✐ã♦ ❞❡ ✐♥t❡r❡ss❡✱ ✭❝✮ ✭δ = 1.30✮ t♦❞♦s ♦s ③❡r♦s ♦❜t✐❞♦s✱
✭❞✮ ✭δ = 1.30✮ ❛♠♣❧✐❛çã♦ ❞❛ r❡❣✐ã♦ ❞❡ ✐♥t❡r❡ss❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✼✳✶ ❘❡❣r❡ssã♦ ❧✐♥❡❛r ♣❛r❛ −ln■♠[u01(L)] ✈❡rs✉s lnL ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s
✈❛❧♦r❡s ❞❡ dν ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡δ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✼✳✷ ❘❡❣r❡ssã♦ ❧✐♥❡❛r ♣❛r❛ −ln■♠[u01(L)] ✈❡rs✉s lnL ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s
✈❛❧♦r❡s ❞❡ dν ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡δ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✼✳✸ ❘❡❣r❡ssã♦ ❧✐♥❡❛r ♣❛r❛ ❘❡β(L)✈❡rs✉sL−1/ν ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s ✈❛❧♦r❡s
❞❡ βc ❡Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✼✳✹ ❘❡❣r❡ssã♦ ❧✐♥❡❛r ♣❛r❛ ❘❡β(L)✈❡rs✉sL−1/ν ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s ✈❛❧♦r❡s
❞❡ βc ❡Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✼✳✺ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❞❡Tc ✈❡rs✉sδ❝♦♥str✉í❞♦ ❛ ♣❛rt✐r ❞❡ ♥♦ss♦s r❡s✉❧t❛❞♦s✳ ✼✶
✼✳✻ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❞❡Tc ✈❡rs✉s δ r❡t✐r❛❞♦ ❞❛ r❡❢✳✭✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
❆✳✶ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.89✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
❆✳✷ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.89✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
❆✳✸ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.91✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
❆✳✹ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.91✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
❆✳✺ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.93✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
❆✳✻ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
①✈ ❆✳✼ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.95✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
❆✳✽ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.95✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
❆✳✾ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.97✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
❆✳✶✵ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 0.97✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
❆✳✶✶ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.00✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
❆✳✶✷ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.00✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹
❆✳✶✸ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.10✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
❆✳✶✹ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.10✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
❆✳✶✺ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.20✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
❆✳✶✻ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.20✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
❆✳✶✼ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦sa(E)✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.30✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
❆✳✶✽ P❛râ♠❡tr♦s ♠✉❧t✐❝❛♥ô♥✐❝♦s b(E) ✜♥❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❞❛❞♦s ♣❛r❛ δ = 1.30✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
❈✳✶ ❈❛❧♦r❡s ❡s♣❡❝í✜❝♦s ♠✐❝r♦❝❛♥ô♥✐❝♦s ♣❛r❛ ✭❛✮δ = 0.89✭❜✮delta = 0.91✱
①✈✐ ❈✳✷ ❈❛❧♦r❡s ❡s♣❡❝í✜❝♦s ♠✐❝r♦❝❛♥ô♥✐❝♦s ♣❛r❛ ✭❛✮δ = 0.97✭❜✮delta = 1.00✱
✭❝✮ δ= 1.10✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼
❈✳✸ δ = 1.20✭❛✮ b(E) ✈❡rs✉s E/N✱ ✭❜✮ ❈❛❧♦r ❡s♣❡❝í✜❝♦ ♠✐❝r♦❝❛♥ô♥✐❝♦✳ ✳ ✳ ✶✵✽
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❉❡✜♥✐çõ❡s ❞❡ ❛❧❣✉♥s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ♣❛r❛ s✐st❡♠❛s ✢✉✐❞♦ ❡ ♠❛❣♥ét✐❝♦✳ ✶✻ ✷✳✷ ❆❧❣✉♠❛s ✐❣✉❛❧❞❛❞❡s ❡♥tr❡ ❡①♣♦❡♥t❡s ❝rít✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✹✳✶ ❉❡♣❡♥❞ê♥❝✐❛ ❞❛ ❧❛r❣✉r❛ ❞❛s ❢❛✐①❛s h ❝♦♠ ❛❝♦♣❧❛♠❡♥t♦ δ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✷ ❖r❞❡♠ ❞❡ tr❛♥s✐çã♦ ❞❛ ❢❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s ♣❛r❛ ❛ ❢❛s❡ t❡tr❛❣♦♥❛❧ ♦❜t✐❞❛s ♥❛ r❡❢✳ ✭✶✷✮ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ δ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✸ ❘❡s✉♠♦ ❞❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ♦❜s❡r✈❛❞❛s ♣❛r❛ ❛❧❣✉♥s ❛❝♦♣❧❛♠❡♥t♦s
δ ❝♦♥❢♦r♠❡ ♦❜t✐❞❛s ❡♠ ❞✐❢❡r❡♥t❡s tr❛❜❛❧❤♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✻✳✶ ❘❡❧❛çã♦ ❡♥tr❡ δ✱ h ❡ ❡♥❡r❣✐❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ✉t✐❧✐③❛❞❛ ♥❛s
s✐♠✉❧❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✻✳✷ ❍✐st♦❣r❛♠❛ ♣❛r❛ ❜❛✐①❛s ❡♥❡r❣✐❛s ❝♦♠L= 12 ♣❛r❛ ǫ= 0.5 ❡ ǫ= 1✳ ✳ ✳ ✺✽
✻✳✸ nM C ✉t✐❧✐③❛❞♦s ♥❛ ♣r♦❞✉çã♦ ❞❡ ❞❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✼✳✶ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❋❙❙ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦✳ ✻✻ ✼✳✷ ❚❡♠♣❡r❛t✉r❛s ❝rít✐❝❛s ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛ ❋❙❙ ♣❛r❛ ❘❡(β)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✼✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ bc(E)❡ βc ♣❛r❛ δ= 1.20❡ 1.30✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
❇✳✶ ❩❡r♦s ♣❛r❛ δ = 0.89✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
❇✳✷ ❩❡r♦s ♣❛r❛ δ = 0.91✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
❇✳✸ ❩❡r♦s ♣❛r❛ δ = 0.93✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
①✈✐✐✐ ❇✳✹ ❩❡r♦s ♣❛r❛ δ = 0.95✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
❇✳✺ ❩❡r♦s ♣❛r❛ δ = 0.97✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
❇✳✻ ❩❡r♦s ♣❛r❛ δ = 1.00✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
❇✳✼ ❩❡r♦s ♣❛r❛ δ = 1.10✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
❇✳✽ ❩❡r♦s ♣❛r❛ δ = 1.20✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈✐✐
✶ ■♥tr♦❞✉çã♦ ✹
✷ ❚r❛♥s✐çõ❡s ❞❡ ❢❛s❡ ✶✶
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷ ❖s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷✳✶ ❘❡❧❛çõ❡s ❡♥tr❡ ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ❆♥á❧✐s❡ ❞❡ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✸ ❩❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ✷✷
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷ ❩❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷✳✶ ❩❡r♦s ❞❡ ❨❛♥❣✲▲❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷✳✷ ❩❡r♦s ❞❡ ❋✐s❤❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ❊s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸✳✶ ●r✉♣♦ ❞❡ r❡♥♦r♠❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸✳✷ ❊s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
❙❯▼➪❘■❖ ✷ ✹ ❖ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❞✐♣♦❧❛r ❜✐❞✐♠❡♥s✐♦♥❛❧ ✸✻
✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✷ ❆ ❤❛♠✐❧t♦♥✐❛♥❛ ❞♦ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✸ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✺ ▼ét♦❞♦s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✹✹
✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✺✳✷ ❊♥s❡♠❜❧❡s ❣❡♥❡r❛❧✐③❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✺✳✷✳✶ ❖ ❛❧❣♦r✐t♠♦ ❡♥tró♣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✳✷✳✷ ❖ ❛❧❣♦r✐t♠♦ ♠✉❧t✐❝❛♥ô♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✷✳✷✳✶ ❊st✐♠❛t✐✈❛s ❝❛♥ô♥✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✷✳✷✳✷ ❘❡❧❛çõ❡s ❞❡ r❡❝♦rrê♥❝✐❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ♣❡s♦
♠✉❧t✐❝❛♥ô♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✻ ❙✐♠✉❧❛çã♦ ❞♦ ♠♦❞❡❧♦ ✺✸
✻✳✶ ❈♦♥❞✐çõ❡s ♣❡r✐ó❞✐❝❛s ❞❡ ❝♦♥t♦r♥♦ ❡ ♦ ♠ét♦❞♦ ❞❛ s♦♠❛ ❞❡ ❊✇❛❧❞ ✳ ✳ ✳ ✺✹ ✻✳✷ ❙✐♠✉❧❛çõ❡s ♠✉❧t✐❝❛♥ô♥✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✻✳✸ ❩❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ❝❛♥ô♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✼ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssã♦ ✻✺
✼✳✶ ❆♥á❧✐s❡ ❞❡ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ✻✻ ✼✳✷ P♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♦✉tr❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✽ ❈♦♥❝❧✉sõ❡s ✼✺
❙❯▼➪❘■❖ ✸
❆ P❛râ♠❡tr♦s ▼✉❧t✐❝❛♥ô♥✐❝♦s ✽✷
❇ ❩❡r♦s ❝♦♠♣❧❡①♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ✶✵✶
❈❛♣ít✉❧♦
1
■♥tr♦❞✉çã♦
❊♥t❡♥❞❡✲s❡ ♣♦r ✜❧♠❡ ✜♥♦ ✉♠❛ ❝❛♠❛❞❛ ❞❡ ♠❛t❡r✐❛❧ q✉❡ ♣♦❞❡ t❡r ❞❡s❞❡ ❢r❛çõ❡s ❞❡ ♥❛♥ô♠❡tr♦ ❛té ✈ár✐♦s ♠✐❝rô♠❡tr♦s ❞❡ ❡s♣❡ss✉r❛✳ ❆s ❛♣❧✐❝❛çõ❡s ❞❡st❡ t✐♣♦ ❞❡ ✜❧♠❡ sã♦ ✈❛st❛s✱ ❡ ❞❡♥tr❡ ❡❧❛s ❡stã♦ ❛ ❢❛❜r✐❝❛çã♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ❡❧❡trô♥✐❝♦s s❡♠✐❝♦♥❞✉t♦r❡s✱ r❡✈❡st✐♠❡♥t♦s ó♣t✐❝♦s ❡ ♠❡♠ór✐❛s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✳ ❋✐❧♠❡s ❞❡ ♠❡t❛❧ s♦❜r❡ ♠❡t❛❧ sã♦ ✉t✐❧✐③❛❞♦s ♥❛ ❡❧❡trô♥✐❝❛✱ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡ ❝❛tá❧✐s❡s✳ ❋✐❧♠❡s ♠♦❧❡❝✉❧❛r❡s tê♠ s✐❞♦ ❛♣❧✐❝❛❞♦s ♥❛ ❜✐♦t❡❝♥♦❧♦❣✐❛ ❡ ❢❛r♠❛❝♦❧♦❣✐❛✳ ❋✐❧♠❡s ♠❛❣♥ét✐❝♦s ✉❧tr❛✜♥♦s✱ q✉❡ tê♠ ❡s♣❡ss✉r❛s ♣ró①✐♠❛s ❛ ✉♠❛ ❝❛♠❛❞❛ ❛tô♠✐❝❛✱ tê♠ s✐❞♦ ❧❛r❣❛♠❡♥t❡ ❡st✉❞❛❞♦s✳ ❈♦♠♦ ❡①❡♠♣❧♦ ♣♦❞❡♠♦s ❝✐t❛r ❞♦✐s t✐♣♦s✿ ✜❧♠❡s ❞❡ ♠❡t❛❧ s♦❜r❡ ♠❡t❛❧✱ ❝♦♠♦ ❢❡rr♦ ❡♠ ❝♦❜r❡ ✭❋❡✴❈♦✮ ✭✶✮ ❡ ❝♦❜r❡ ❡♠ ♦✉r♦ ✭❈♦✴❆✉✮ ✭✷✮✱ ❡ ✜❧♠❡s ❞❡ ❝❡râ♠✐❝❛s s✉♣❡r❝♦♥❞✉t♦r❛s ❝♦♠♦ ♦ ❘✲❇❛✲❈✉✱ ♦♥❞❡ ❘ é t❡rr❛✲r❛r❛ ❞❛ sér✐❡ ❞♦s ❧❛♥t❛♥í❞❡♦s✳ ❆s ♠✉❞❛♥ç❛s✱ t❛♥t♦ ♥♦ ❝♦♥t❡ú❞♦ ❞❡ ♦①✐❣ê♥✐♦ ❝♦♠♦ ♥❛ ❝♦♠♣♦s✐çã♦ ❞❡ss❛s ❝❡râ♠✐❝❛s✱ tê♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥❛ ❞❡✜♥✐çã♦ ❞❡ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦ s✉♣❡r❝♦♥❞✉t♦r✱ ✐s♦❧❛♥t❡ ♦✉ ♠❛❣♥ét✐❝♦ ✭✸✮✳ ❆ ♣r♦❞✉çã♦ ❡ ✉t✐❧✐③❛çã♦ ❞❡ ✜❧♠❡s ✉❧tr❛✜♥♦s tê♠ s✐❞♦ ♣♦ssí✈❡❧ ❣r❛ç❛s ❛♦ ❛✈❛♥ç♦ ♥❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♠❛t❡r✐❛✐s ❡♠ ❡s❝❛❧❛ ❛tô♠✐❝❛ ✭♥❛♥♦t❡❝♥♦❧♦❣✐❛✮✱ ❝♦♠ té❝♥✐❝❛s ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡ ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ❝❛❞❛ ✈❡③ ♠❡❧❤♦r❡s✳ ❊♠❜♦r❛ ❤❛❥❛ ✉♠ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥❛ ❛♣❧✐❝❛çã♦ t❡❝♥♦❧ó❣✐❝❛✱ ♦ ❡st✉❞♦ t❡ór✐❝♦ ❞❡ss❡s ✜❧♠❡s ♣❡r♠✐t❡ ✉♠❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞❛s ✐♥t❡r❛çõ❡s ❛tô♠✐❝❛s✳ ❊ss❛ ❝♦♠♣r❡❡♥sã♦ é s❡♠ ❞ú✈✐❞❛ ❞❡ ❡①tr❡♠❛ ✐♠♣♦rtâ♥❝✐❛✳ ❖ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠❛t❡r✐❛✐s ♣❛r❛ ✉s♦ ❡s♣❡❝í✜❝♦ r❡q✉❡r ✉♠ ❡♥t❡♥❞✐♠❡♥t♦ ❞❡t❛❧❤❛❞♦ ❞❛s ✐♥t❡r❛çõ❡s ♠✐❝r♦s❝ó♣✐❝❛s ❡ ❞❡ ❝♦♠♦ ❡ss❛s sã♦ ❛❢❡t❛❞❛s ♣❡❧❛ ❝♦♠♣♦s✐çã♦ ❡ ♣r❡♣❛r❛çã♦✱ r❡s✉❧t❛♥❞♦ ♥❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠❛t❡r✐❛❧✳ ❖ ✉s♦ ❞❡ ✜❧♠❡s ♠❛❣♥ét✐❝♦s ♣❛r❛ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❞❛❞♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ❡①✐❣❡ q✉❡ ❛ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ✜❧♠❡ s❡❥❛ ❞❡✜♥✐❞❛ ❡ ❧✐❞❛ ❝♦♠ ❛❧t♦ ❣r❛✉ ❞❡ ❛❝✉rá❝✐❛ ❡ r❡s♦❧✉çã♦
✶ ✲ ■♥tr♦❞✉çã♦ ✺
❋✐❣✉r❛ ✶✳✶✿ ❋❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s ❝♦♠ ❧❛r❣✉r❛ h= 4✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ✭✹✮✳
❡s♣❛❝✐❛❧ ✭✶✮✳
❋✐❧♠❡s ♠❛❣♥ét✐❝♦s ✉❧tr❛✜♥♦s ❛♣r❡s❡♥t❛♠ ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ♥ã♦ ✉s✉❛✐s✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ t❡♠♣❡r❛t✉r❛ ❛❝✐♠❛ ❞❛ q✉❛❧ ❛ ♠❛❣♥❡t✐③❛çã♦ ♦❝♦rr❡ ♥❛ ❞✐r❡çã♦ ❞♦ ♣❧❛♥♦ ❞♦ ✜❧♠❡✱ ❡ ❛❜❛✐①♦ ❞❡st❛✱ ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ♣❧❛♥♦✳ P❛r❛ ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣❡r❛t✉r❛ ❡♠ q✉❡ ♦❝♦rr❡ ❛ ♠❛❣♥❡t✐③❛çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r✱ sã♦ ♦❜s❡r✈❛❞❛s ❢❛s❡s ❝♦♠ ❞♦♠í♥✐♦s t✐♣♦ ❢❛✐①❛s✱ ♦♥❞❡ ♦ s✐st❡♠❛ é ❝♦♥st✐t✉í❞♦ ♣♦r ❢❛✐①❛s ❛❧t❡r♥❛❞❛s ❢❡rr♦♠❛❣♥ét✐❝❛s ✭✈❡❥❛ ❛ ✜❣✉r❛ ✶✳✶✮✱ ♥❛ ❢♦r♠❛ ❞❡ ❧❛❜✐r✐♥t♦s✱ ❞❡♥tr❡ ♦✉tr❛s✳ ❊ss❛s ❢❛s❡s✱ ❛♣❡s❛r ❞❡ ❛♣r❡s❡♥t❛r❡♠ ♠❛❣♥❡t✐③❛çã♦ t♦t❛❧ ♣r❛t✐❝❛♠❡♥t❡ ♥✉❧❛✱ ❛♣r❡s❡♥t❛♠ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ♦r❞❡♥❛♠❡♥t♦✳
✶ ✲ ■♥tr♦❞✉çã♦ ✻
❋✐❣✉r❛ ✶✳✷✿ ❉✐❢❡r❡♥t❡s ❢❛s❡s ♦❜s❡r✈❛❞❛s ❡♠ ✜❧♠❡s ✜♥♦s ❞❡ ❋❡ ❡♠ ❈✉ ♣❡❧❛ té❝♥✐❝❛ ❙❊▼P❆ ✭♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛ ❝♦♠ ❛♥á❧✐s❡ ❞❡ ♣♦❧❛r✐③❛çã♦✮✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ✭✺✮
sã♦ ❝♦♥st✐t✉í❞♦s ❞❡ ✉♠❛ ú♥✐❝❛ ❝❛♠❛❞❛✱ r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ q✉❡ ❝♦♥s✐❞❡r❛✱ ❛❧é♠ ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ❡♥tr❡ ♣r✐♠❡✐r♦s ✈✐③✐♥❤♦s✱ ❛ ✐♥t❡r❛çã♦ ❞✐♣♦❧❛r ❡♥tr❡ t♦❞♦s ♦s s♣✐♥s✳ ❖ ❡❢❡✐t♦ ❝♦♥❥✉♥t♦ ❞❛ ✐♥t❡r❛çã♦ ❞✐♣♦❧❛r ❞❡ ❧♦♥❣♦ ❛❧❝❛♥❝❡ ❝♦♠ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ❞❡ ❝✉rt♦ ❛❧❝❛♥❝❡ ❝♦♥❞✉③ ❛♦ ❢❡♥ô♠❡♥♦ ❞❡ ❢r✉str❛çã♦ ❡ ❡①♣❧✐❝❛ ❛ ♦r✐❣❡♠ ❞❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ✐♥t❡r❡ss❛♥t❡s ❡ ✐♥❝♦♠✉♥s ❢❡♥ô♠❡♥♦s ♠❛❣♥ét✐❝♦s✳ ❆ ❤❛♠✐❧t♦♥✐❛♥❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛s ✐♥t❡r❛çõ❡s ❡♥tr❡ s♣✐♥s ♥❡ss❡ s✐st❡♠❛ é ❞❛❞❛ ♣♦r
E(σ) =−δ X <i,j>
σiσj +X
i6=j σiσj
r3
ij
, ✭✶✳✶✮
♦♥❞❡ δ = J/g é ❛ r❛③ã♦ ❡♥tr❡ ♦s ❛❝♦♣❧❛♠❡♥t♦s ❞❛s ✐♥t❡r❛çõ❡s ❞❡ tr♦❝❛ ✭J > 0✮ ❡
❞✐♣♦❧❛r ✭g > 0✮✳ ❖ ♣r✐♠❡✐r♦ t❡r♠♦ r❡♣r❡s❡♥t❛ ♦ t❡r♠♦ ❞❡ ■s✐♥❣ s✐♠♣❧❡s✱ q✉❡ ❧❡✈❛
❡♠ ❝♦♥t❛ s♦♠❡♥t❡ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♣r✐♠❡✐r♦s ✈✐③✐♥❤♦s✳ ❖ s❡❣✉♥❞♦ t❡r♠♦ r❡♣r❡s❡♥t❛ ❛ ✐♥t❡r❛çã♦ ❞✐♣♦❧❛r ❡ ❧❡✈❛ ❡♠ ❝♦♥t❛ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ t♦❞♦s ♦s ♣❛r❡s ❞❡ s♣✐♥s✳ ❖ ♠ét♦❞♦ ❞❛ s♦♠❛ ❞❡ ❊✇❛❧❞ ✭✻✱ ✼✮✱ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ❧✐❞❛r ❝♦♠ ✐♥t❡r❛çõ❡s ❞❡ ❧♦♥❣♦ ❛❧❝❛♥❝❡✱ ❥á t❡♠ s✐❞♦ ✉t✐❧✐③❛❞♦ ♣♦r ♥♦ss♦ ❣r✉♣♦ ❞❡ ♣❡sq✉✐s❛ ✭✽✮ ♥❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛s ❝♦♥❞✐çõ❡s ♣❡r✐ó❞✐❝❛s ❞❡ ❝♦♥t♦r♥♦ ♣❛r❛ ❛s ✐♥t❡r❛çõ❡s ❞✐♣♦❧❛r❡s✳ ❆ ✜❣✉r❛ ✶✳✸ ✐❧✉str❛ ❛s três ❢❛s❡s ♦❜s❡r✈❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s ❡♠ s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✉s❛♥❞♦ δ = 2✳ ◆❡st❛ ✜❣✉r❛ t❡♠♦s ❛s ❢❛s❡s ❞♦ t✐♣♦ ❢❛✐①❛s✱ ♥❡♠át✐❝❛ ❡ t❡tr❛❣♦♥❛❧✳
✶ ✲ ■♥tr♦❞✉çã♦ ✼
❋✐❣✉r❛ ✶✳✸✿ ❈♦♥✜❣✉r❛çõ❡s ❞♦s s♣✐♥s ♣❛r❛ ✉♠❛ r❡❞❡ ❞❡ ❧❛r❣✉r❛L = 56 ♦❜t✐❞❛s ♣♦r
s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❡♠ t❡♠♣❡r❛t✉r❛s q✉❡ ❛♣r❡s❡♥t❛♠✿ ✭❛✮ ❢❛s❡ t✐♣♦ ❢❛✐①❛s✱ ✭❜✮ ♥❡♠át✐❝❛ ❡ ✭❝✮ t❡tr❛❣♦♥❛❧✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❛ r❡❢✳ ✭✶✸✮✳
♣❛rt❡s ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❛✐♥❞❛ ♥ã♦ ❛♣r❡s❡♥t❛♠ ✐♥❞✐❝❛çõ❡s ❝♦♥❝❧✉s✐✈❛s ❞❛ ♦r❞❡♠ ❞❛s tr❛♥s✐çõ❡s✱ ♦✉ s❡❥❛✱ ♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❞♦ ♠♦❞❡❧♦ ❛✐♥❞❛ ♥ã♦ é ❝♦♠♣❧❡t❛♠❡♥t❡ ❝♦♥❤❡❝✐❞♦✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ♣♦♥t♦ tr✐❝rít✐❝♦ ❡♥tr❡δ= 0.89❡ δ= 1
é ♣r❡✈✐st❛ ♣♦r ♠ét♦❞♦s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✭✶✶✮✱ ♠❛s s✉❛ ❧♦❝❛❧✐③❛çã♦ ♣r❡❝✐s❛ ❛✐♥❞❛ ♥ã♦ é ❝♦♥❤❡❝✐❞❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♣r❡t❡♥❞❡♠♦s ✐♥✈❡st✐❣❛r ❛ ❡①✐stê♥❝✐❛ ❞❡ss❡ ♣♦♥t♦ tr✐❝rít✐❝♦ ❡ ❛ss✐♠✱ ❞❡✜♥✐r ❡ss❛ ♣❛rt❡ ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡✳
❉✐✈❡r❣ê♥❝✐❛s ❡♥tr❡ ❛s ♣r❡❞✐çõ❡s ♣♦r ♠ét♦❞♦s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❡ ❝á❧❝✉❧♦s ❞❡ ❈❛♠♣♦ ▼é❞✐♦ ❝♦❧♦❝❛♠ ❡♠ ❞ú✈✐❞❛ ❛ ❡①✐stê♥❝✐❛ ❞❛ ❢❛s❡ ✐♥t❡r♠❡❞✐ár✐❛ ♥❡♠át✐❝❛✱ ❡①✐st❡♥t❡ ❡♥tr❡ ❛ ❢❛s❡ ❞♦ t✐♣♦ ❢❛✐①❛s ❡ ❛ ❢❛s❡ t❡tr❛❣♦♥❛❧✱ ♣❛r❛ ♦ ✐♥t❡r✈❛❧♦ ❞♦ ❛❝♦♣❧❛♠❡♥t♦ δ
♥♦ q✉❛❧ ❡st❛♠♦s tr❛❜❛❧❤❛♥❞♦ ✭δ ∈[0.89−1.20]✮✳ ❖s ③❡r♦s ❝♦♠♣❧❡①♦s ❞❛ ❢✉♥çã♦ ❞❡
♣❛rt✐çã♦ ♣❡r♠✐t❡♠ ❝❛r❛❝t❡r✐③❛r ❛ ❝r✐t✐❝❛❧✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛ ❡✱ ♣♦r✐ss♦✱ ❧❛♥ç❛♠♦s ♠ã♦ ❞♦ s❡✉ ✉s♦ ♥❛ ❜✉s❝❛ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ♣♦♥t♦ tr✐❝rít✐❝♦ ❡ ❛ss✐♠ ♣♦❞❡r ❝❛r❛❝t❡r✐③❛r ♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ♥❛ r❡❣✐ã♦ ❞❡ ✐♥t❡r❡ss❡✳ ❱❛❧❡ s❛❧✐❡♥t❛r q✉❡ ♦ ♠♦❞❡❧♦ ❡♠ q✉❡stã♦ ❛✐♥❞❛ ♥ã♦ ❢♦✐ ❡st✉❞❛❞♦ ✈✐❛ ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦✳
✶ ✲ ■♥tr♦❞✉çã♦ ✽ t❡r♠♦❞✐♥â♠✐❝❛s ♣♦❞❡ s❡r r❡✈❡❧❛❞♦ s❡ ♦❧❤❛r♠♦s ♣❛r❛ ♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦✳ ❈♦♠ ❡ss❡ ❡♥❢♦q✉❡✱ ♣✉❞❡r❛♠ ♦❜t❡r ✉♠❛ ❞❡s❝r✐çã♦ ❞❛s ❢❛s❡s ❝♦♥❞❡♥s❛❞❛s ❞♦ ❣ás ❡ ❞❛s r❡❣✐õ❡s ❞❡ tr❛♥s✐çã♦ ♥♦ ❧✐♠✐t❡ t❡r♠♦❞✐♥â♠✐❝♦✳ ◆♦ ♠❡s♠♦ tr❛❜❛❧❤♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♦ ❚❡♦r❡♠❛ ❞♦ ❈ír❝✉❧♦✳ ❊st❡ t❡♦r❡♠❛ ❞✐③ q✉❡ ♦s ③❡r♦s✱ ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❡①t❡r♥♦ ♦❝♦rr❡♠ ❡♠ ✉♠ ❝ír❝✉❧♦ ✉♥✐tár✐♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ❊♥q✉❛♥t♦ ❨❛♥❣ ❡ ▲❡❡ ❝♦♥s✐❞❡r❛r❛♠ ♦s ③❡r♦s ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❛r❛ s✐st❡♠❛s ❞❡ s♣✐♥s✱ ❋✐s❤❡r ✭✶✽✮ ❡♠ ✶✾✻✺ ❝❤❛♠♦✉ ❛t❡♥çã♦ ♣❛r❛ ❛ r❡❧❡✈â♥❝✐❛ ❞♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ❯s❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ♣❛r❛ r❡❞❡s ❜✐❞✐♠❡♥s✐♦♥❛✐s ❝♦♠ ❣❡♦♠❡tr✐❛ q✉❛❞r❛❞❛ ❝♦♠♦ ❡①❡♠♣❧♦✱ ❡❧❡ ♠♦str♦✉ q✉❡ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ❡r❛♠ ❞✐str✐❜✉í❞♦s ❡♠ ❞✉❛s ❝✉r✈❛s ❢❡❝❤❛❞❛s ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ♥♦ ❧✐♠✐t❡ t❡r♠♦❞✐♥â♠✐❝♦ ❡ q✉❡ ❛ s✐♥❣✉❧❛r✐❞❛❞❡ ❧♦❣❛rít♠✐❝❛ ❞♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡r✐✈❛✈❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ss❡s ③❡r♦s✳ ❊♥tr❡t❛♥t♦✱ ♥ã♦ t❡♠♦s ✉♠ t❡♦r❡♠❛ ❞♦ ❝ír❝✉❧♦ ♣❛r❛ ♦s ③❡r♦s ❞❡ ❋✐s❤❡r✱ ❞❛❞♦ q✉❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ss❡s ③❡r♦s ❞❡♣❡♥❞❡ ❢♦rt❡♠❡♥t❡ ❞♦s ❞❡t❛❧❤❡s ❞♦ s✐st❡♠❛✳ ❆ ❛✉sê♥❝✐❛ ❞❡ ✉♠ r❡s✉❧t❛❞♦ ❣❡r❛❧ ♣❛r❛ ♦s ③❡r♦s ❞❡ ❋✐s❤❡r s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ q✉❡ ❛ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛ é ✉♠❛ q✉❛♥t✐❞❛❞❡ q✉❡ ✈❛r✐❛ ❞❡ ✉♠ s✐st❡♠❛ ♣❛r❛ ♦✉tr♦ ✭✷✷✮✳ ■♥❞❡♣❡♥❞❡♥t❡ ❞♦ ♠♦❞❡❧♦ ❛ s❡r ❡st✉❞❛❞♦✱ s❛❜❡♠♦s q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ③❡r♦s ♣ró①✐♠♦ ❛♦ ❡✐①♦ r❡❛❧ ♣♦s✐t✐✈♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❡t❡r♠✐♥❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❝rít✐❝♦✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ t❡♠ s✐❞♦ ❜❛st❛♥t❡ ❡①♣❧♦r❛❞❛ ❡♠ ✐♥ú♠❡r♦s s✐st❡♠❛s t❡r♠♦❞✐♥â♠✐❝♦s✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ t❡♠♣❡r❛t✉r❛ ❡ ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s✳
✶ ✲ ■♥tr♦❞✉çã♦ ✾
❋✐❣✉r❛ ✶✳✹✿ ❍✐st♦❣r❛♠❛s ❞❡ ❡♥❡r❣✐❛ ♦❜t✐❞♦s ❞❡ ✉♠❛ s✐♠✉❧❛çã♦ ♠✉❧t✐❝❛♥ô♥✐❝❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ❤✐st♦❣r❛♠❛s r❡♣❡s❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s ♥♦ ❡♥s❡♠❜❧❡ ❝❛♥ô♥✐❝♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ✷❞ ❡♠ ✉♠❛ r❡❞❡20×20✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭✷✻✮✳
❛❧❣♦r✐t♠♦ ♠✉❧t✐❝❛♥ô♥✐❝♦ ❝❛r❛❝t❡r✐③❛✲s❡ ♣♦r ♣r♦❝✉r❛r ❛♠♦str❛r t♦❞❛s ❛s ❡♥❡r❣✐❛s ❝♦♠ ❛ ♠❡s♠❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦ ❤✐st♦❣r❛♠❛ ♦❜t✐❞♦ s❡❥❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✉♥✐❢♦r♠❡✳ ❉❡st❛ ♠❛♥❡✐r❛✱ ❝♦♥✜❣✉r❛çõ❡s ✐♠♣♦rt❛♥t❡s ♠❛s r❛r❛s ♥♦ ❡♥s❡♠❜❧❡ ❝❛♥ô♥✐❝♦ sã♦ ❛♠♦str❛❞❛s✱ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠ q✉❡ ❜❛rr❡✐r❛s ❞❡ ❡♥❡r❣✐❛ ❧✐✈r❡ s❡❥❛♠ ✉❧tr❛♣❛ss❛❞❛s✳ ❖✉tr❛ ✈❛♥t❛❣❡♠ ❞♦ ❛❧❣♦r✐t♠♦ ♠✉❧t✐❝❛♥ô♥✐❝♦ é q✉❡✱ ❡♥q✉❛♥t♦ ❛s s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ♥♦ ❡♥s❡♠❜❧❡ ❝❛♥ô♥✐❝♦ sã♦ ❡❢❡t✉❛❞❛s ❛ ✉♠❛ t❡♠♣❡r❛t✉r❛ ✜①❛ ❡ só ♣♦❞❡♠ s❡r ❡①tr❛♣♦❧❛❞❛s ♣❡❧❛ té❝♥✐❝❛ ❞❡ r❡♣❡s❛❣❡♠ ♣❛r❛ t❡♠♣❡r❛t✉r❛s ❜❡♠ ♣ró①✐♠❛s à t❡♠♣❡r❛t✉r❛ s✐♠✉❧❛❞❛✱ ❛s s✐♠✉❧❛çõ❡s ♥♦ ❡♥s❡♠❜❧❡ ♠✉❧t✐❝❛♥ô♥✐❝♦ ♣❡r♠✐t❡♠ ♦ ❝á❧❝✉❧♦ ❞❡ ✈❛❧♦r❡s ❡s♣❡r❛❞♦s ❝❛♥ô♥✐❝♦s ❡♠ q✉❛❧q✉❡r t❡♠♣❡r❛t✉r❛✳ ❆ ✜❣✉r❛ ✶✳✹ ❛♣r❡s❡♥t❛ ♦s ❤✐st♦❣r❛♠❛s ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ es ✭E/N ✲ ❡♥❡r❣✐❛ t♦t❛❧ ❞✐✈✐❞✐❞❛ ♣❡❧♦
♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ❞♦ s✐st❡♠❛✮ ♦❜t✐❞♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ■s✐♥❣ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ✉♠❛ r❡❞❡ q✉❛❞r❛❞❛ 20×20 ♣❛r❛ ✉♠❛ s✐♠✉❧❛çã♦ ♠✉❧t✐❝❛♥ô♥✐❝❛✳ ❖ ❤✐st♦❣r❛♠❛
❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✉♥✐❢♦r♠❡✱ q✉❡ ❛❜r❛♥❣❡ ✉♠ ♠❛✐♦r ✐♥t❡r✈❛❧♦ ❞❡ ❡♥❡r❣✐❛✱ é ♦ ♦❜t✐❞♦ ❞✐r❡t❛♠❡♥t❡ ❞❛s s✐♠✉❧❛çõ❡s ♠✉❧t✐❝❛♥ô♥✐❝❛s ❡ ♦s ♦✉tr♦s três ❤✐st♦❣r❛♠❛s sã♦ ♦s ❤✐st♦❣r❛♠❛s r❡♣❡s❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ β = 1/kBT✱ ❞❛❞♦ ❡♠ ✉♥✐❞❛❞❡s
❞❡kB ♦♥❞❡ T é ❛ t❡♠♣❡r❛t✉r❛ ❞♦ s✐st❡♠❛✳
✶ ✲ ■♥tr♦❞✉çã♦ ✶✵ ❝♦♥s✐❞❡r❛❞♦✳ ❊ss❡s ❡❢❡✐t♦s sã♦ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ✐♠♣♦rt❛♥t❡s ♥❛s r❡❣✐õ❡s ❝rít✐❝❛s✳ ❙❡ ✈❛r✐❛r♠♦s ♦ t❛♠❛♥❤♦ ❞♦ s✐st❡♠❛ ♥❛s s✐♠✉❧❛çõ❡s✱ ♣♦❞❡♠♦s ✉t✐❧✐③❛r ❛ t❡♦r✐❛ ❞❡ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦ ✜♥✐t♦ ✭❋✐♥✐t❡ ❙✐③❡ ❙❝❛❧✐♥❣ ✲ ❋❙❙✮✳ ❊st❛ t❡♦r✐❛ é ✉t✐❧✐③❛❞❛ ❡♠ s✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ♣❛r❛ ❡st✐♠❛r ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ♥❛s ❣r❛♥❞❡③❛s t❡r♠♦❞✐♥â♠✐❝❛s ❝♦♠♦ ❝❛❧♦r ❡s♣❡❝í✜❝♦✱ ♣♦r ❡①❡♠♣❧♦✳ ◆♦ ♣♦♥t♦ ❝rít✐❝♦✱ ❛ t❛①❛ ❞❡ ✈❛r✐❛çã♦ ❞❛s ❢✉♥çõ❡s t❡r♠♦❞✐♥â♠✐❝❛s ❞✐✈❡r❣❡ ❡ ❛ss✉♠❡ ❛ ❢♦r♠❛ t✐♣♦ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛ ❝♦♠ ❡①♣♦❡♥t❡s✱ ❝❤❛♠❛❞♦s ❞❡ ❡①♣♦❡♥t❡s ❝rít✐❝♦s✱ q✉❡ ❞❡♣❡♥❞❡♠ ❛♣❡♥❛s ❞❡ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ s✐st❡♠❛✳ ◆♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✉t✐❧✐③❛r❡♠♦s r❡❧❛çõ❡s ❞❡ ❡s❝❛❧❛ ♣❛r❛ ♦s ③❡r♦s ❞❛ ❢✉♥çã♦ ❞❡ ♣❛rt✐çã♦ ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♦❜t❡r♠♦s ❛ ♦r❞❡♠ ❞❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❡ ❛ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛ ❡♠ ❢✉♥çã♦ ❞❡ ✈ár✐♦s ✈❛❧♦r❡s ❞♦ ❛❝♦♣❧❛♠❡♥t♦δ✳
❈❛♣ít✉❧♦
2
❚r❛♥s✐çõ❡s ❞❡ ❢❛s❡
✷✳✶ ■♥tr♦❞✉çã♦
◆❡st❡ ❝❛♣ít✉❧♦ ✈❡r❡♠♦s ❛ ❞❡✜♥✐çã♦ ❞❡ tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ❞❡ ♣r✐♠❡✐r❛ ❡ s❡❣✉♥❞❛ ♦r❞❡♠ ❡ ❛ r❡❧❛çã♦ ❝♦♠ ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s✳ ❚♦❞♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ ❝❛♣ít✉❧♦ ❢♦✐ ❜❛s❡❛❞♦ ♥❛ r❡❢❡rê♥❝✐❛ ✭✷✼✮✳ ❱❡r❡♠♦s t❛♠❜é♠ q✉❡✱ ❛♣❡s❛r ❞❛s s✐♠✉❧❛çõ❡s s❡r❡♠ ❡❢❡t✉❛❞❛s ❡♠ s✐st❡♠❛s ✜♥✐t♦s✱ ♣♦❞❡♠♦s ♦❜t❡r ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ❡ ❛ ♦r❞❡♠ ❞❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❡s♣❡r❛❞♦s ♥♦ ❧✐♠✐t❡ t❡r♠♦❞✐♥â♠✐❝♦ ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞❡ ❋❙❙✳ ❈♦♠ r❡❧❛çã♦ à ♦r❞❡♠ ❞❡ ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡✱ ❝♦♥s✐❞❡r❡♠♦s ♦ ❝r✐tér✐♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ❊❤r❡♥❢❡st ❡ t♦♠❡♠♦s ❝♦♠♦ ❡①❡♠♣❧♦ ❛ ❡♥❡r❣✐❛ ❧✐✈r❡ ❞❡ ❍❡❧♠❤♦❧t③ F✳ ❙❡ s✉❛
♣r✐♠❡✐r❛ ❞❡r✐✈❛❞❛ é ❞❡s❝♦♥tí♥✉❛✱ t❡♠♦s ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❙❡ ❛ ♣r✐♠❡✐r❛ ❞❡r✐✈❛❞❛ ❢♦r ❝♦♥tí♥✉❛✱ ♠❛s ❛ s❡❣✉♥❞❛ ❢♦r ❞❡s❝♦♥tí♥✉❛✱ t❡♠♦s ✉♠❛ tr❛♥s✐çã♦ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✱ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛♠❡♥t❡✳ ❯♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✱ t❛♠❜é♠ ❝❤❛♠❛❞❛ ❞❡ tr❛♥s✐çã♦ ❝♦♥tí♥✉❛✱ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ♣♦♥t♦ ❝rít✐❝♦ ♥♦ ❞✐❛❣r❛♠❛ ❞❡ ❢❛s❡✳ P❛r❛ ✉♠❛ tr❛♥s✐çã♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ t❡♠♦s ❣❡r❛❧♠❡♥t❡ ✉♠❛ ❞❡s❝♦♥t✐♥✉✐❞❛❞❡ ♥❛ ❡♥tr♦♣✐❛✱ ♦✉ s❡❥❛✱ ✉♠❛ ❞❡s❝♦♥t✐♥✉✐❞❛❞❡ ♥❛ ♣r✐♠❡✐r❛ ❞❡r✐✈❛❞❛ ❞♦ ♣♦t❡♥❝✐❛❧ t❡r♠♦❞✐♥â♠✐❝♦✱
S =
∂F ∂T
. ✭✷✳✶✮
❯♠❛ ❞❛s ❢♦r♠❛s ❞❡ s❡ ♦❜t❡r ❛ ♦r❞❡♠ ❞❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ é ♦❜s❡r✈❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❞♦ s✐st❡♠❛✳ ❯♠ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ é ✉♠❛ ✈❛r✐á✈❡❧ ❡①t❡♥s✐✈❛ q✉❡ ♣❡r♠✐t❡ ❞✐st✐♥❣✉✐r ❛s ❞✐❢❡r❡♥t❡s ❢❛s❡s ❞♦ s✐st❡♠❛ ❡ ♣♦r ❝♦♥✈❡♥✐ê♥❝✐❛✱ ❣❡r❛❧♠❡♥t❡ é ❡s❝♦❧❤✐❞♦ ❞❡ ❢♦r♠❛ q✉❡ s❡❥❛ ♥✉❧♦ ♥❛ ❢❛s❡ ❞❡s♦r❞❡♥❛❞❛✳
✷✳✶ ✲ ■♥tr♦❞✉çã♦ ✶✷ ❈♦♥s✐❞❡r❛♥❞♦ F(H, T) ♣❛r❛ ✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦✱ ♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❡♠
r❡❧❛çã♦ ❛♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ H é ❞❛❞♦ ♣♦r φ=−
∂F ∂H
,
❡ ♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❡♠ r❡❧❛çã♦ ❛ t❡♠♣❡r❛t✉r❛ T é ❛ ❡♥tr♦♣✐❛ S ✭❞❛❞❛
❛♥t❡r✐♦♠❡♥t❡ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✶✮✳ ❙❡ ♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❢♦r ❞❡s❝♦♥tí♥✉♦ ❡♠ r❡❧❛çã♦ à ✈❛r✐á✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❡ ✭❝♦♥s✐❞❡r❡♠♦s ❝♦♠♦ ❡①❡♠♣❧♦ ❛ ✈❛r✐á✈❡❧ T✮✱ t❡♠♦s
✉♠❛ tr❛♥s✐çã♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❊♠ ✉♠❛ tr❛♥s✐çã♦ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✱ ♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ t❡♠ s✐♥❣✉❧❛r✐❞❛❞❡s q✉❡ ♦❜❡❞❡❝❡♠ r❡❧❛çõ❡s t✐♣♦ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛✱
φ∝
Tc−T Tc β , ✭✷✳✷✮
❛ss✐♠ ❝♦♠♦ ♦ ❝❛❧♦r ❡s♣❡❝í✜❝♦ ❡ ❛ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛✱
cH =−T
∂2F
∂T2 H ∝
Tc−T Tc −α , ✭✷✳✸✮
χ=−
∂2F
∂H2 T ∝
Tc−T Tc −γ , ✭✷✳✹✮
♦♥❞❡β✱ α ❡ γ sã♦ ♦s ❝❤❛♠❛❞♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s✳
P❛r❛ ✐❧✉str❛r ❝♦♠ ♠❛✐♦r ❝❧❛r❡③❛ tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ❞❡ ♣r✐♠❡✐r❛ ❡ s❡❣✉♥❞❛ ♦r❞❡♠✱ ✉t✐❧✐③❛r❡♠♦s ❝♦♠♦ ❡①❡♠♣❧♦ ❞♦✐s t✐♣♦s ❞❡ s✐st❡♠❛✿ ✉♠ s✐st❡♠❛ ✢✉✐❞♦ ❡ ✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦ s✐♠♣❧❡s✳ P❛r❛ ♦ s✐st❡♠❛ ✢✉✐❞♦✱ ❛ ❡q✉❛çã♦ ❞❡ ❡st❛❞♦ f(P, ρ, T) = 0✱
r❡❧❛❝✐♦♥❛♥❞♦ ❛ ♣r❡ssã♦ P✱ ❞❡♥s✐❞❛❞❡ ρ ❡ ❛ t❡♠♣❡r❛t✉r❛ T✱ ❞❡✜♥❡ ✉♠❛ s✉♣❡r❢í❝✐❡
❡♠ três ❞✐♠❡♥sõ❡s ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ❡st❛❞♦s ❞❡ ❡q✉✐❧í❜r✐♦✳ ❆♥❛❧♦❣❛♠❡♥t❡ ♣❛r❛ ✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦✱ t❡♠♦s ✉♠❛ ❡q✉❛çã♦ ❞❡ ❡st❛❞♦g(H, M, T)r❡❧❛❝✐♦♥❛❞❛ ❛♦ ❝❛♠♣♦
♠❛❣♥ét✐❝♦ H✱ à ♠❛❣♥❡t✐③❛çã♦ M ❡ à t❡♠♣❡r❛t✉r❛ T✳ ❱❛♠♦s ❝♦♥s✐❞❡r❛r ❛❣♦r❛ ❛s
♣r♦❥❡çõ❡s ❞❛s s✉♣❡r❢í❝✐❡s P ρT ❡ HM T ♥♦s ♣❧❛♥♦s P T ❡ HT✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ♣❛r❛
✷✳✶ ✲ ■♥tr♦❞✉çã♦ ✶✸
❋✐❣✉r❛ ✷✳✶✿ ✭❛✮ ❉✐❛❣r❛♠❛P T ♣❛r❛ ✉♠ s✐st❡♠❛ ✢✉✐❞♦✳ ✭❜✮ ❉✐❛❣r❛♠❛ HT ♣❛r❛ ✉♠
s✐st❡♠❛ ♠❛❣♥ét✐❝♦ s✐♠♣❧❡s✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭✷✼✮✳
❝rít✐❝♦✱ ❞❛❞♦ ♣❡❧❛s ❝♦♦r❞❡♥❛❞❛s Pc✱ Tc ❡ ρc✳ ❆ ♣❛rt✐r ❞❡ss❡ ♣♦♥t♦ ♥ã♦ ❤á ❞✐❢❡r❡♥ç❛
❢✉♥❞❛♠❡♥t❛❧ ❡♥tr❡ ❛s ❢❛s❡s ❧íq✉✐❞❛ ❡ ❣❛s♦s❛✳ ◆♦ ❝❛s♦ ♠❛❣♥ét✐❝♦✱ ♦❜s❡r✈❛♠♦s q✉❡ ❡①✐st❡♠ ❞✉❛s ❢❛s❡s✿ ❛ ❢❡rr♦♠❛❣♥ét✐❝❛ ❡ ❛ ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝❛ q✉❡ ❡stã♦ ❡♠ ❡q✉✐❧í❜r✐♦ ❡♠ ✉♠❛ ❝✉r✈❛ q✉❛♥❞♦ H = 0✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♥♦ s✐st❡♠❛ ✢✉✐❞♦✱ ❛ ❝✉r✈❛
❞❡ tr❛♥s✐çã♦ t❡r♠✐♥❛ ♥♦ ♣♦♥t♦ ❝rít✐❝♦ ❛ss♦❝✐❛❞♦ às ❝♦♦r❞❡♥❛❞❛s Hc✱ Tc ❡ Mc✱ ❞❡
♠♦❞♦ q✉❡ ❛ ♣❛rt✐r ❞❡ t❛❧ ♣♦♥t♦ ♥ã♦ ❤á ❞✐st✐♥çã♦ ❡♥tr❡ ❛s ❞✉❛s ❢❛s❡s✳ ❖❧❤❛♥❞♦ ❛❣♦r❛ ♣❛r❛ ♦s ♣❧❛♥♦s ρT ❡ M T ✭✜❣✉r❛ ✷✳✷✮✱ t❡♠♦s ♣❛r❛ ♦ s✐st❡♠❛ ✢✉✐❞♦ ✉♠❛
❞✐❢❡r❡♥ç❛ s✐❣♥✐✜❝❛t✐✈❛ ❡♥tr❡ ❛s ❞❡♥s✐❞❛❞❡s ❞♦ ❧íq✉✐❞♦ ✭ρL✮ ❡ ❞♦ ❣ás ✭ρG✮ ♣❛r❛ ❜❛✐①❛s
t❡♠♣❡r❛t✉r❛s✳ ❈♦♥❢♦r♠❡ ❛ t❡♠♣❡r❛t✉r❛ ❛✉♠❡♥t❛ ❡ s❡ ❛♣r♦①✐♠❛ ❞❡ Tc✱ ♠❡♥♦r é
❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ρL −ρG✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ ♣❛r❛ ♦ s✐st❡♠❛ ♠❛❣♥ét✐❝♦ t❡♠♦s q✉❡✱
❝♦♥❢♦r♠❡ ❛ t❡♠♣❡r❛t✉r❛ ❛✉♠❡♥t❛ ♣❛r❛ ♣ró①✐♠♦ ❞❡Tc✱ ❛ ♠❛❣♥❡t✐③❛çã♦ s❡ ❛♣r♦①✐♠❛
❞❡0✳ ◆♦t❡ q✉❡ ρL−ρG ❡ M sã♦ ♦s ♣❛râ♠❡tr♦s ❞❡ ♦r❞❡♠ ♣❛r❛ ♦s s✐st❡♠❛s ✢✉✐❞♦ ❡
✷✳✷ ✲ ❖s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ✶✹
❋✐❣✉r❛ ✷✳✷✿ ✭❛✮ ❉✐❛❣r❛♠❛ ρT ♣❛r❛ ✉♠ s✐st❡♠❛ ✢✉✐❞♦ ♣✉r♦✳ ✭❜✮ ❉✐❛❣r❛♠❛ M T ♣❛r❛
✉♠ s✐st❡♠❛ ♠❛❣♥ét✐❝♦ s✐♠♣❧❡s✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭✷✼✮✳
❝♦♥tí♥✉❛s ❞❡ s✐st❡♠❛s ❞✐❢❡r❡♥t❡s✳ ❉✐③❡♠♦s q✉❡ ❞♦✐s s✐st❡♠❛s ♣❡rt❡♥❝❡♠ à ♠❡s♠❛ ❝❧❛ss❡ ❞❡ ✉♥✐✈❡rs❛❧✐❞❛❞❡ s❡ ❢♦r♥❡❝❡♠ ♦ ♠❡s♠♦ ❝♦♥❥✉♥t♦ ❞❡ ❡①♣♦❡♥t❡s✳ ❱❡r❡♠♦s ♥❛ ♣ró①✐♠❛ s❡çã♦ ❛ ♦r✐❣❡♠ ❞♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s✳
✷✳✷ ❖s ❡①♣♦❡♥t❡s ❝rít✐❝♦s
❖s ❡st✉❞♦s ❞♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ✐♥✐❝✐❛r❛♠✲s❡ ♣♦r ✈♦❧t❛ ❞❡ ✶✾✻✵ ❝♦♠ ❍❡❧❧❡r ❡ ❇❡♥❡❞❡❝❦✱ ❏❛❝r♦t ❡ ♦✉tr♦s✳ ❆té ✶✾✹✺✱ ❛❝r❡❞✐t❛✈❛✲s❡ q✉❡ ❛ ❝✉r✈❛ ❞❡ ❝♦❡①✐stê♥❝✐❛ ❞❡ ✉♠ s✐st❡♠❛ ✢✉✐❞♦ ❡r❛ ♣❛r❛❜ó❧✐❝❛✳ ❍❛✈✐❛ t❛♠❜é♠ ✉♠❛ ♣r❡❞✐çã♦ ❞❡ q✉❡ ♣❛r❛ s✐st❡♠❛s ♠❛❣♥ét✐❝♦s M2 ∝ (Tc−T)✳ ❊♥tr❡t❛♥t♦✱ ❛s ♠❡❞✐❞❛s ❞❡ ❍❡❧❧❡r ❡ ❇❡♥❡❞❡❝❦
♠♦str❛r❛♠ q✉❡M3 ∝(Tc−T)❡ ❛s ♠❡❞✐❞❛s ❞❡ ●✉❣❣❡♥❤❡✐♠ ♠♦str❛r❛♠ q✉❡ T
Tc
3
∝ ρcρ
✭✜❣✉r❛ ✷✳✸✮ ♣❛r❛ ✈ár✐♦s ❣❛s❡s✳ ❈♦♥s✐❞❡r❡♠♦s ♦ ❝❛s♦ ♠❛❣♥ét✐❝♦✱ s❡♥❞♦M ♦ ♣❛râ♠❡tr♦
❞❡ ♦r❞❡♠✱ ❡st❡ ✈❛r✐❛ ❝♦♠ (−ǫ)β✱ ♦♥❞❡ ǫ ≡ T −Tc
Tc ✳ ❉❡ss❛ ❢♦r♠❛✱ β = 1/3 é ♦
❡①♣♦❡♥t❡ ❝rít✐❝♦ ❛ss♦❝✐❛❞♦ à ♠❛❣♥❡t✐③❛çã♦ ❞♦ s✐st❡♠❛✳ ❙❡ ✉♠❛ r❡❧❛çã♦ ❞❛ ❢♦r♠❛M =
B(−ǫ)β é ✈á❧✐❞❛✱ ❡♥tã♦ ❛❧❣✉♠❛s ♠❡❞✐❞❛s ♣ró①✐♠❛s ❛♦ ♣♦♥t♦ ❝rít✐❝♦ sã♦ s✉✜❝✐❡♥t❡s
♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ ✈❛❧♦r ❞❡ β✳ ❆ ♣❛rt✐r ❞❡ ❡♥tã♦✱ ♦s ❡①♣♦❡♥t❡s ❝rít✐❝♦s ❝♦♠❡ç❛r❛♠
❛ s❡r ✉t✐❧✐③❛❞♦s ♣❛r❛ ❞❡s❝r❡✈❡r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✈ár✐❛s q✉❛♥t✐❞❛❞❡s ❞❡ ✐♥t❡r❡ss❡ ♣ró①✐♠♦ ❛♦ ♣♦♥t♦ ❝rít✐❝♦✳
