Criticality of Lamellar Surfaces by Conformational Degrees of Freedom

Abstract

A new model for lamellar surfaces formed by anisotropic molecules is proposed. The molecules have internal degrees of freedom, associated with their flexible section of length $N$ at zero temperature. We obtain a 2D non-standard six vertex model, which is exactly soluble and exhibits a finite order transition. The order and the character of the transition are determined by the dominant term in the $1 \over N$-expansion of the interaction energy. The dependence of the critical temperatures on $N$ is, instead, determined by the non-leading terms in the same expansion.