NEW REAL-SPACE RENORMALIZATION TECHNIQUES AND THEIR APPLICATION TO MODELS OF VARIOUS SPIN AND SPACE DIMENSIONALITIES

The mean-field approximation is used for the evaluation of the Niemeijer-Van Leeuwen real-space renormalization. Although this new method is very simple, it gives reasonable results for the critical properties of two-, three-, and four-dimensional Ising models, for the transition temperature Tc of an Ising model with clusters and for the two-dimensional Ising antiferromagnet in an external magnetic field. Using this new mean-field renormalization in connection with the real-space renormalization of the kinetic Ising model, which recently has been suggested by the author, we obtain the long-time relaxation of the magnetization for all temperatures above Tc. In the last application the critical properties of n-dimensional spins in two and three space dimensions are calculated for arbitrary n. Here the mean-field approximation and Monte Carlo methods are used to evaluate the renormalization step. © 1979 The American Physical Society.