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

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be σ  =  -0.37(6), in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes σ  =  -0.32(4). 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.