Bethe approximation for self-interacting lattice trees

In this paper we develop a Bethe approximation, based on the cluster variat ion method, which is apt to study lattice models of branched polymers. We s how 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 latt ice trees on a graph coincide with analogous expressions derived through di fferent approaches. We study the phase diagram of lattice trees with neares t-neighbour attraction and branching energies. We find a collapse transitio n at a tricritical theta paint, which separates an expanded phase from a co mpact phase. We compare our results for the theta transition in two and thr ee dimensions with available numerical estimates.