Nuclear Physics B251[FSI31 (1985) 665-675 9 North-Holland Publishing Company MONTE CARLO METItOD FOR RANDOM SURFACES B. BERG IL hlstitut f~r Theoretische Physik der Unieersitgtt llamburg, Luruper Chaussee 149, D-2000 llamburg 50 A. BILLOIRE Service de Physique Thborique, Orme des Merisiers. CEN-SACI~t Y, 91191 Gif-sur-Yeette, Cedex, France D. FOERSTER Max-Planck hlstitut, Fohringer Ring 6. D8000 Mfinchen 40, West Germany Received 1 June 1984 Previously two of the authors proposed a Monte Carlo method for sampling statistical ensembles of random walks and surfaces with a Boltzmann probabilistic weight. In the present paper we work out the details for several models of random surfaces, defined on d-dimensional hypercubic lattices. 1. Introduction Random surfaces have attracted a lot of interest [1], because of their relation to relativistic string theory, non-abelian gauge theories and problems in statistical mechanics. Only few analytic results exist and numerical studies may be very useful. In ref. [2] a local stochastic process was proposed, which allows one to generate statistical ensembles of walks and surfaces with a Boltzmann probabilistic weight. If applicable the procedure allows Monte Carlo (MC) simulations of rather large walks and surfaces, because the needed amount of computer memory is only proportional to the length of the walk, respectively the area of the surface. The MC procedure of ref. [2] (MCP2) has a wide range of possible applications. For instance one may carry out a stochastic inversion of large matrices, which are relevant for fermions in lattice QCD. Kuti [3] advocated later the von Neumann-Ulam method for similar purposes. A test is the stochastic computation of the average of y-traces (Tr)L over walks of fixed length L (for thd precise definition of Tl:t. see ref. [4]). In table 1 we compare the exact answer [4] with results as obtained by the MCP 2 [5] and by the von Neumann-Ulam method [6]. The MCP2 is more efficient because