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International Journal of Modern Physics C

DYNAMICAL CRITICAL BEHAVIOR OF THE FOUR-DIMENSIONAL ISING MODEL

Joan Adler, Dietrich Stauffer

Published Dec 1, 1996• 6 citations
Publisher

Abstract

Monte Carlo simulations of the Glauber dynamics in the four-dimensional Ising model with up to 3124 spins agree with the theoretically expected logarithmic corrections to mean field behavior, if we assume J/kBTc = 0.14970, consistent with some series analysis.
DOI
10.1142/s0129183195000666

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The four-dimensional Ising model is studied to probe the possibility of observing in Monte Carlo simulations the logarithmic corrections to the mean-field theory near criticality. The finite-size-scaling behavior for the correlation length is proposed. The scaling forms of the finite-size renormalized coupling, susceptibility, and fourth field derivative at the renormalized tree-level approximation are derived. These results are used to analyze simulation data of the simple hypercubic lattices of sizes 4\ensuremath{\le}L\ensuremath{\le}14, near criticality. Our simulation results are in agreement with the presence of logarithmic corrections and recent field-theoretical calculations of the specific heat. The approach to the nonscattering theory is observed and is consistent with the predicted logarithmic finite-size dependence.
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