The Magnetization of the 3D Ising Model

Abstract

We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to $256^3$ spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose computer for the Wolff cluster simulation of the 3D Ising model. We find that the magnetization $M(t)$ is perfectly described by $M(t)=(a_0-a_1{t}^{\theta }-a_{2}t)t^{\beta }$, where $t=(T_{\mathrm{c}}-T)/T_{\mathrm{c}}$, in a wide temperature range $0.0005<t<0.26$. If there exist corrections to scaling with higher powers of $t$, they are very small. The magnetization exponent is determined as $\beta =0.3269$ (6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: $K_{\mathrm{c}}=J/k_B{T}_{\mathrm{c}}=0.2216544$, with a standard deviation of $3\cdot 10^{-7}$.

Comments: 7 pages, 5 Postscript figures