2 3 Ja n 20 06 Test of Universality in Anisotropic 3 D Ising Model

Chen and Dohm predicted theoretically in 2004 that the widely believed universality principle is violated in the Ising model on the simple cubic lattice with more than only six nearest neighbours. Schulte and Drope by Monte Carlo simulations found such violation, but not in the predicted direction. Selke and Shchur tested the square lattice. Here we check only this univer-sality for the susceptibility ratio near the critical point. For this purpose we study first the standard Ising model on a simple cubic lattice with six nearest neighbours, then with six nearest and twelve next-nearest neighbours, and compare the results with the Chen-Dohm lattice of six nearest neighbours and only half of the twelve next-nearest neighbours. We do not confirm the violation of universality found by Schulte and Drope in the susceptibility ratio. 1. Introduction To study the critical phenomena of any system, all systems are divided [1] into a small number of universality classes. They are characterized by the dimensionality of the space and the number of components of the order parameter. Within a certain universality class, the universal quantities (critical exponents, amplitude ratios, and scaling functions) are independent of microscopic details, such as the particular type of interactions or lattice structure. Once the universal quantities of a universality class are known, the asymp-totic critical behavior of very different systems (e.g. fluids and magnets) is believed to be known completely provided that only two nonuniversal amplitudes and the non-universal critical temperature T c are given.