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 compute r 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 c riticality 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).