SYSTEMATIC ENUMERATION OF CONFIGURATION CLASSES FOR ENTROPIC SAMPLING OF ISING MODELS

Bruno Jeferson Lourenço () and Ronald Dickman ()
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Bruno Jeferson Lourenço: Departamento de Física, Instituto de Ciências Exatas and National Institute of Science and Technology for Complex Systems, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil
Ronald Dickman: Departamento de Física, Instituto de Ciências Exatas and National Institute of Science and Technology for Complex Systems, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil

International Journal of Modern Physics C (IJMPC), 2012, vol. 23, issue 08, 1-12

Abstract: We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic (AF) Ising model in an external magnetic field on the square lattice, which is simulated using the tomographic entropic sampling (TES) algorithm. We estimate the number of configurations,Ω(E,m,L), and related microcanonical averages, for all allowed energiesEand magnetizationsmforL = 10to 30, withΔL = 2. With prior knowledge of the CCs, we can be sure that all allowed classes are sampled during the simulation. Complete enumeration of CCs also enables us to use the final estimate ofΩ(E,m,L)to obtain good initial estimates,Ω0(E,m,L′), for successive system sizes(L′ > L)through a two-dimensional interpolation. Using these results we calculate canonical averages of the thermodynamic quantities of interest as continuous functions of temperatureTand external fieldh. In addition, we determine the critical line in theh-Tplane using finite-size scaling analysis, and compare these results with several approximate theoretical expressions.

Keywords: Ising model; antiferromagnet; configuration classes; Monte Carlo simulation; phase diagram; 11.25.Hf; 123.1K (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0129183112400074

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