A Monte Carlo Sampling Scheme for the Ising Model

• DOI: 10.1023/b:joss.0000003116.17579.5d
• Publication Date: 2003-11-14T20:35:11Z
• Authors: Roland Häggkvist; Anders Rosengren; Daniel Andrén; Petras Kundrotas; Per Håkan Lundow; Klas Markström
• Keywords: Rejection sampling; Metropolis–Hastings algorithm; Monte Carlo integration

In this paper we describe a Monte Carlo sampling scheme for the Ising model and similar discrete-state models. The scheme does not involve any particular method of state generation but rather focuses on a new way of measuring and using the Monte Carlo data. We show how to reconstruct the entropy S of the model, from which, e.g., the free energy can be obtained. Furthermore we discuss how this scheme allows us to more or less completely remove the effects of critical fluctuations near the critical temperature and likewise how it reduces critical slowing down. This makes it possible to use simple state generation methods like the Metropolis algorithm also for large lattices.