Fixed-Connectivity Membranes

TL;DR

This paper reviews the statistical mechanics of flexible membranes, highlighting their elastic properties, shape fluctuations, and universal negative Poisson ratio, with discussions on crystalline order and self-avoidance effects.

Contribution

It provides a comprehensive summary of membrane physics, emphasizing the universal negative Poisson ratio and crystalline order in spherical membranes, integrating various membrane models.

Findings

Universal negative Poisson ratio in phantom and self-avoiding membranes

Crystalline order on spherical membrane surfaces

Insights into shape fluctuations and elasticity

Abstract

The statistical mechanics of flexible surfaces with internal elasticity and shape fluctuations is summarized. Phantom and self-avoiding isotropic and anisotropic membranes are discussed, with emphasis on the universal negative Poisson ratio common to the low-temperature phase of phantom membranes and all strictly self-avoiding membranes in the absence of attractive interactions. The study of crystalline order on the frozen surface of spherical membranes is also treated.