IMPROVED ALGORITHMS FOR SIMULATING CRYSTALLINE MEMBRANES

The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. Numerical simulations ar e commonly used to study this class of models. Unfortunately, traditio nal Monte Carlo algorithms suffer from very long auto-correlation time s, especially near critical points. In this paper we study the perform ance of improved Monte Carlo algorithms for simulating crystalline mem brane, such as hybrid overrelaxation and unigrid methods, and compare their performance to the more traditional Metropolis algorithm. We fin d that although the overrelaxation algorithm does not reduce the criti cal slowing down, it gives an overall gain of a factor 15 over the Met ropolis algorithm. The unigrid algorithm does, on the other hand, redu ce the critical slowing down exponent to z approximate to 1.7. (C) 199 8 Elsevier Science B.V.