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 ≃ − 0.32 on a 128 2 lattice at bending rigidity κ = 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.