The Poisson ratio of crystalline surfaces

A remarkable theoretical prediction for a crystalline (polymerized) surface is that its Poisson ratio sigma is negative. Using a large-scale Monte Carlo simulation of a simple model of such surfaces we show that this is indeed true. The precise numerical value we find is sigma similar or equal to -0.32 on a 128(2) lattice at bending rigidity kappa = 1.1. This is in excellent agreement with the prediction sigma = -1/3 following from the self-consistent screening approximation of Le Doussal and Radzihovsky.