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The Poisson ratio of crystalline surfaces

A remarkable theoretical prediction for a crystalline (polymerized) surface is that its Poisson ratio (σ) 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 (σ\simeq -0.32) on a (128^2) lattice at bending rigidity (kappa = 1.1). This is in excellent agreement with the prediction (σ= -1/3) following from the self-consistent screening approximation of Le Doussal and Radzihovsky.