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Loop expansion around the Bethe–Peierls approximation for lattice models

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Published 8 February 2006 IOP Publishing Ltd
, , Citation Giorgio Parisi and František Slanina J. Stat. Mech. (2006) L02003 DOI 10.1088/1742-5468/2006/02/L02003

1742-5468/2006/02/L02003

Abstract

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe–Peierls approximation appears naturally as the saddle-point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetization and correlation function.

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10.1088/1742-5468/2006/02/L02003