Multicanonical Potts Model Simulation

Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes 100 × 100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to L. Thus the computational effort as counted per degree of freedom for generating an independent configuration in the unstable region of the model rises proportional to V , where V is the volume of the system. On our largest lattice we gain more than two orders of magnitude as compared to a standard heat bath algorithm. As a first physical application we report a high precision computation of the interfacial tension. This research project was partially funded by the National Science Foundation under grant INT-8922411 and by the the Department of Energy under contract DE-FG05-87ER40319 Fakultät für Physik, Universität Bielefeld, D-4800 Bielefeld, FRG Supercomputer Computations Research Institute Tallahassee, FL 32306, USA 4 On leave of absence from Department of Physics, The Florida State University, Tallahassee, USA. Critical slowing down is of crucial importance to computer simulations of phase transitions. For second order phase transitions long autocorrelation times at criticality cause severe restrictions on the maximum lattice size for which one can obtain good statistics of thermodynamic quantities. For a number of spin systems this critical slowing down was overcome by the nonlocal cluster algorithm of Swendsen-Wang [1], for a recent review see [2]. However, for first order transition one encounters an even worse and different problem of critical slowing down. The interfacial free energy between disordered and ordered states has a finite value on the critical point for the infinite volume system. Configurations dominated by the presence of the interface will be exponentially suppressed by the Boltzmann factor in the canonical ensemble. On finite lattices this leads then to an exponentially fast suppression of the tunneling between metastable states of the system with increasing lattice size. To overcome this critical slowing down effect for first order transitions, we recently proposed a multicanonical Monte Carlo algorithm [3]. The multicanonical MC algorithm is designed to enhance configurations, which are dominated by the presence of the interface and therefore exponentially suppressed. In this way it is possible to avoid the exponentially fast growing slowing down at the first order phase transition. In this paper we demonstrate this in the case of our example: the 2d 10-state Potts model. The 2d 10-state Potts model [4] is defined by the partition function