Solution of a model of SAW's with multiple monomers per site on the Husimi lattice

TL;DR

This paper presents an exact solution of a self-avoiding walk model on the Husimi lattice allowing for double visits per site, revealing a phase diagram with two polymerized phases and critical points, relevant for polymer collapse transitions.

Contribution

It introduces a solvable Husimi lattice model for SAWs with multiple monomers per site, extending previous Bethe lattice results to include phase diagram details.

Findings

Two polymerized phases identified

Presence of a tricritical point and a critical endpoint

Phase diagram similar to Bethe lattice solution

Abstract

We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers with one-site interactions only. We consider the version in which immediate self-reversals of the walk are forbidden (RF model). The phase diagram we obtain for the grand-canonical version of the model is similar to the one found in the solution of the Bethe lattice, with two distinct polymerized phases, a tricritical point and a critical endpoint.