Experimental investigation of the logarithmic correction to the mean-field order parameter of the four-dimensional Ising ferromagnet

Abstract

The order parameter $\Phi$ of the four-dimensional simple hypercubic spin-½ Ising ferromagnet is calculated by the Monte Carlo technique. The data, which may be represented by $\Phi \mathrm{}\left(t\right)=B{\mathrm{}(-t)\mathrm{}}^{\frac{1}{2}}{\left|\ln \mathrm{}\right(-t\left)\right|}^{\frac{1}{3}}$ with $1.53<B<\mathrm{}1.56\mathrm{}$ for $0.005<-t\equiv \frac{(T_c-T)}{T_c}<0.40\mathrm{}$, supports the theoretical prediction of a multiplicative logarithmic correction to the mean-field description of the critical behavior in four dimensions.