Solution of a model of self-avoiding walks with multiple monomers per site on the Bethe lattice

TL;DR

This paper analytically solves a self-avoiding walk model with up to two monomers per site on the Bethe lattice, revealing complex phase diagrams including first-order and tricritical transitions relevant to polymer collapse.

Contribution

It introduces and solves a novel lattice model of self-avoiding walks with multiple monomers per site, exploring effects of self-reversal restrictions on phase behavior.

Findings

Phase diagram with polymerized and non-polymerized phases.

First-order phase transition when immediate self-reversals are allowed.

Rich phase structure including tricritical point and critical endpoint when reversals are forbidden.

Abstract

We solve a model of self-avoiding walks with up to two monomers per site on the Bethe lattice. This model, inspired on the Domb-Joyce model, was recently proposed to describe the collapse transition observed in interacting polymers [J. Krawczyk et al, Phys. Rev. Lett. 96, 240603 (2006)]. When immediate self-reversals are allowed (RA model), the solution displays a phase diagram with a polymerized phase and a non-polymerized phase, separated by a phase transition which is of first order for a non-vanishing statistical weight of doubly occupied sites. If the configurations are restricted forbidding immediate self-reversals (RF model), a richer phase diagram is found, displaying a tricritical point and a critical endpoint.