Loop expansion around the Bethe-Peierls approximation for lattice models

Giorgio Parisi, Frantisek Slanina

Published 2005-12-21Version 1

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 magnetisation and correlation function.