Critical properties and finite-size effects of the five-dimensional Ising model

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 (the temperature variation of which near the critical temperatureT _c is |1-T/T _c |^–1/2), but rather with a thermodynamic lengthl (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.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday