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doi: 10.6062/jcis.2011.02.02.0034(Free PDF)

Leandro G. Rizzi and Nelson A. Alves

Several studies to determine the nature of the thermodynamic phase transitions for an Ising model for ultrathin magnetic films have been reported in recent years. No conclusive results have been obtained yet, because the simulation with conventional Monte Carlo methods is slowed down by long relaxation times due to the suppression of tunneling events through free energy barriers. In this paper we study the Ising model with dipolar interactions in two dimensions with an generalized-ensemble algorithm to address this problem. Herein, the multicanonical algorithm has been implemented in this work because it systematically explores energy configurations and enhances the rate of tunneling events. The success of a simulation depends on how often the algorithm explores the energy range between two extremal values. Our results indicate a limitation of the multicanonical algorithm in estimating the density of states for this model because the algorithm does not satisfactorily circumvent the problem of high free energy barriers in the energy region where the nematic phase takes place.

computational physics and chemistry, multicanonical algorithm, dipolar Ising model, free-energy barrier.

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