The magnetization of the 3D Ising model

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 spontaneous magnetization M(t) is accurately described by M(t) = (a(0) - a(1)t(beta) - a(2)t)t(beta) where t = (T-c - T)/T-c, 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 beta = 0.3269(6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: K-c = J/k(B)T(c) = 0.2216544, with a standard deviation of 3 x 10(-7).