Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase

TL;DR

This paper investigates the universal properties of crystalline membranes, focusing on the crumpling transition and Poisson ratio in the flat phase, using large-scale simulations to provide precise critical exponents and confirm theoretical predictions.

Contribution

It provides the first large-scale Monte Carlo simulation analysis of the crumpling transition and Poisson ratio in crystalline membranes, confirming universality and auxetic behavior.

Findings

Identified a continuous crumpling transition with accurate critical exponents.

Computed the asymptotic Poisson ratio in the flat phase, confirming universality.

Validated theoretical predictions for polymerized membranes with fixed connectivity.

Abstract

We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques. By controlling the scaling corrections, we additionally compute with high accuracy the asymptotic value of the Poisson ratio in the flat phase, thus characterizing the auxetic properties of this class of systems. We obtain agreement with the value which is universally expected for polymerized membranes with a fixed connectivity.