Bethe approximation for self-interacting lattice trees

Details Bethe approximation for self-interacting lattice trees Bethe approximation for self-interacting lattice trees

2000-11-15

arxiv.org/abs/cond-mat/0011258v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 3 figures, to be published in Europhysics Letters

Scientific paper

In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover, the expressions we obtain for the asymptotic number of spanning trees and lattice trees on a graph coincide with analogous expressions derived through different approaches. We study the phase diagram of lattice trees with nearest-neighbour attraction and branching energies. We find a collapse transition at a tricritical theta point, which separates an expanded phase from a compact phase. We compare our results for the theta transition in two and three dimensions with available numerical estimates.

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