PROPERTIES OF ITERATIVE MONTE CARLO SINGLE HISTOGRAM REWEIGHTING

Martin Gmitra () and Denis Horváth ()
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Martin Gmitra: Department of Theoretical Physics and Astrophysics, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic
Denis Horváth: Department of Theoretical Physics and Astrophysics, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 12, 1943-1952

Abstract: We present an iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The ferromagnetic 2D Ising model is studied numerically as an illustration. In that case, the iterations reach a stationary regime with an invariant probability distribution function of temperature which peaked near the pseudocritical temperature of the specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting the variance of pseudocritical temperature and the parameter of linear filtering.

Keywords: Monte Carlo; histogram reweighting; autoregressive model; 02.70.Tt; 05.50.+q; 02.50.Ey; 05.65.+b (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105008606

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