In a recent paper Hoede and Zandvliet introduced the concept of gauging on an equation. This enables the simulation of more complex Ising models by the simple quadratic model. The possibility of simulating the simple cubic model was defended by calculating a sequence of approximations to the transition point from a so-called solution function.
In this paper we investigate some aspects of such a simulation, in particular with respect to the solution. It is also shown that taking into account the difference in universality class is possible. It is argued that the critical exponent for the specific heat is 0. The theory then also leads to a choice of the other critical exponents, depending on the validity of the scaling hypothesis of Widom and experimental data. Using the value 3/8 for the critical exponent for the magnetization we establish a relationship between the transition equations of the 2D and the 3D model.
|Place of Publication
|University of Twente
|Number of pages
|Published - Sept 2008
|Department of Applied Mathematics, University of Twente