Abstract
An expansion for generating functionals (partition sums) of models expressed as lattice functional integrals with local (on-site) interactions is presented. This expansion renormalizes the standard perturbative expansion in such a way that certain its terms are summed up non-perturbatively. A non-self-consistent and a self-consistent versions of the expansion are formulated and criteria for an estimation of validity of approximations resulting from the both expansions are given. The simplest approximation being the first term of this expansion is applied to two lattice models: classicalN-component spin model and the model of non-interacting electrons in a disordered crystal. In the former model the critical temperature is calculated within 10% accuracy and in the latter, the coherent potential approximation is obtained.
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I am grateful to Drs. B. Velický, V. Drchal, J. Mašek, and J. Kudrnovský for encouraging and illuminating discussions. J. Mašek and V. Drchal are also acknowledged for careful reading of the manuscript.
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Janiš, V. Renormalized expansions for functional integrals: Generalized coherent potential approach to lattice models. Czech J Phys 36, 1107–1129 (1986). https://doi.org/10.1007/BF01959604
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DOI: https://doi.org/10.1007/BF01959604