Journal
PHYSICAL REVIEW E
Volume 80, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.031104
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Funding
- High Performance Computing Center North (HPC2N)
- Center for Parallel Computers (PDC)
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In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent alpha = 0 but a nonrigorous 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 are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical 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.
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