A real space renormalisation transformation for lattice systems

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Abstract
The transformation is tested on the two-dimensional Ising model. The transformation is formed by compounding the decimation and Legendre transformations, as suggested by van Leeuwen (1975). The Legendre transformation involves an adjustable parameter p. The cluster approximation is used, as well as a decoupling approximation which is exact in the limit of p to 1. The procedure is seen to be capable of estimating both the thermal and magnetic critical exponents, v and eta respectively, for two-dimensional systems. The accuracy obtained is compared to that of other methods and the applicability of the procedure to three-dimensional systems is discussed.