Volume 53, Number 2, January 2001
|Page(s)||176 - 182|
|Published online||01 December 2003|
Bethe approximation for self-interacting lattice trees
Institut de Physique Theorique, Université de Fribourg
Chemin du Musée 3, CH-1700 Fribourg, Switzerland
2 Department of Mathematics, Imperial College 180 Queen's Gate, London SW7 2BZ, UK
3 Dipartimento di Fisica, Politecnico di Torino - c. Duca degli Abruzzi 24, 10129 Torino and INFM Unità Torino Politecnico - Torino, Italy
Accepted: 13 November 2000
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 θ point, which separates an expanded phase from a compact phase. We compare our results for the θ transition in two and three dimensions with available numerical estimates.
PACS: 05.70.Fh – Phase transitions: general studies / 36.20.Ey – Conformation / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems
© EDP Sciences, 2001
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.