Short-range correlations in magnetic systems: Effective-cluster approach

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Abstract
We present a cluster method that allows the inclusion of short-range correlations into the calculation of the properties of magnetic systems described by a Heisenberg Hamiltonian. The system under consideration is broken up into clusters. The clusters are assumed to be uncorrelated and acted upon by an effective Hamiltonian which approximates the effect of intercluster interaction. The parameters of this effective Hamiltonian are chosen so as to find an optimal upper bound for the free energy. When the cluster consists of only one site we recover molecular-field theory. For the specific systems studied here we find that, for larger clusters, we can recast the method in a form which resembles mean-field theory. We use one-site, two-site, and four-site clusters to apply the method to the spin-(1/2 Heisenberg antiferromagnet on a square lattice. Our results are in agreement with direct diagonalization and Monte Carlo calculations in larger clusters.