Universal Negative Poisson Ratio of Self-Avoiding Fixed-Connectivity Membranes

Abstract

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be $\sigma =-0.37\mathrm{}\left(6\right)$, in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes $\sigma =-0.32\mathrm{}\left(4\right)$. Together with the equality of critical exponents, this result implies a unique universality class for fixed-connectivity membranes. Our findings thus establish that physical fixed-connectivity membranes provide a wide class of auxetic (negative Poisson ratio) materials with significant potential applications in materials science.