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Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study

M. M. Tsypin·H. W. J. Blöte
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Abstract

We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate approximate formula describing the universal shape of P(M).

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M. M. Tsypin, H. W. J. Blöte. 1999-09-23. Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study. https://doi.org/10.1103/physreve.62.73

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