Abstract
Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length ξ (the temperature variation of which near the critical temperatureT c is ξ∝|1-T/T c |−1/2), but rather with a “thermodynamic length”l (withl∝|1-T/T c |−2/d,d=5 here). The susceptibility (extrapolated to the thermodynamic limit) agrees quantitatively with high temperature series extrapolations of Guttmann. The problem of fluctuation corrections to the leading (Landau-like) critical behaviour is briefly discussed, and evidence given for a specific-heat singularity of the form |1-T/T c |1/2, superimposed on its leading jump.
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Recent analytical results (J. Zinn-Justin, private communication) suggest however, that one should haveb=0. This implies that there must still some systematic deviations from finite size scaling due to correction terms be present also in Fig. 13, which are not resolved due to statistical scatter. Then the true scaling function would be slightly shifted to the left from where it is drawn in Fig. 13 [e.g.,g L (0)≈−0.81 instead ofg L (0)≈−1.0]. In view of the corrections to scaling seen in other quantities, this possibility certainly cannot be ruled out
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Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday
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Binder, K. Critical properties and finite-size effects of the five-dimensional Ising model. Z. Physik B - Condensed Matter 61, 13–23 (1985). https://doi.org/10.1007/BF01308937
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DOI: https://doi.org/10.1007/BF01308937