Critical behaviour of the Ising model on the 4-dimensional lattice

Abstract

In this paper we investigate the nature of the singularity of the Ising model of the 4-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent $\alpha =0$ but a non-rigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at $T_c$. We find that within the given accuracy the canonical ensemble data is consistent both with a logarithmic singularity and a bounded specific heat, but that the micro-canonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field theory prediction of a logarithmic singularity is wrong.

5 pages, 7 figures

References in corpus (5)

• Ising spins coupled to a four-dimensional discrete Regge skeleton
• Comparison of perturbative RG theory with lattice data for the 4d Ising model
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
• Repairing Stevenson's step in the 4d Ising model
• Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

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