Decimation transformations for two-dimensional Ising spin systems

Abstract

The decimation transformation is used to calculate critical exponents for two-dimensional Ising spin systems on the square, triangular and hexagonal lattices. Both cumulant and cluster approximations are used. While the results of the low-order cumulant and of small cluster calculations agree well with the known exact exponents, an increase in cluster size does not appear to increase accuracy. The decimation transformation is only found to be useful for calculating thermal eigenvalues.