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

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).

6 pages, 6 Postscript figures, uses RevTeX

References in corpus (7)

• Critical Exponents of the N-vector model
• The universality class of the electroweak theory
• Scaling corrections: site-percolation and Ising model in three dimensions
• The Deconfinement Phase Transition in One-Flavour QCD
• Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model
• The effective potential, critical point scaling and the renormalization group
• Cutoff and lattice effects in the $\varphy^4$ theory of confined systems

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