Resumo: Um dos problemas clássicos em mecânica estatística estudados por Onsager (1949) é o de cilindros colocados numa caixa com interações apenas de volume excluído. No caso tridimensional e contínuo, ele concluiu que se a razão de aspecto (comprimento/raio) fosse suficientemente grande, a densidades altas o sistema apresenta uma ordem nemática, ou seja, os cilindros tendem a se orientar preferencialmente numa direção. Modelos desse tipo são relevantes no estudo de cristais líquidos. Outros pioneiros também estudaram esse problema, como Flory (1956) e Zwanzig (1963). A transição de uma fase isotrópica para outra nemática em 3d para modelos contínuos hoje é bem conhecida, o mesmo modelo em 2d não apresenta transição de fase, o que é uma consequência do teorema de Mermin- Wagner. O comportamento de modelos discretos, onde as varetas são segmentos colineares de k sitios numa rede não é, ainda, bem conhecido. Um trabalho simulacional de Dhar (2007) mostrou que na rede quadrada existe uma fase nemática para densidades intermediárias de ocupação da rede para k igual ou superior a 7. A densidades muito baixas ou muito altas as varetas não têm ordem orientacional. Vamos apresentar resultados recentes sobre esse modelo: a sua resolução numa rede aleatória do tipo Bethe [1] e simulações utilizando um novo algoritmo de Monte-Carlo grande canônico que permite acessar a transição de alta densidade [2].
[1] D. Dhat, R. Rajesh, J. Stilck, Phys. Rev. E 84, 011140 (2011).
[2] J. Kundu, R. Rajesh, D. Dhar e J Stilck, Phys. Rev. E 87, 032103 (2013).
Discussão
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