The magnetization of the 3D Ising model

S.L. Talapov and H.W.J. Blote

J. Phys. A: Math. Gen. 29 (1996) 5727-5733

Abstract:

We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to   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 spontaneous magnetization M(t) is accurately described by  , where  , in a wide temperature range 0.0005 < t < 0.26. Any corrections to scaling with higher powers of t could not be resolved from our data, which implies that they are very small. The magnetization exponent is determined as . An analysis of the magnetization distribution near criticality yields a new determination of the critical point:  , with a standard deviation of  .