Polymers with attractive interactions on the Husimi tree

TL;DR

This paper solves models of self-avoiding walks with attractive interactions on Husimi lattices, revealing complex phase diagrams with multiple phases, transitions, and critical points depending on interaction strength and lattice coordination.

Contribution

It provides an exact solution for self-avoiding walk models with attractions on Husimi lattices, exploring rich phase behavior and phase transitions.

Findings

Two phases (polymerized and non-polymerized) for q>4.

Continuous and first-order phase transitions separated by tricritical points.

Additional dense polymerized phase for q=4 with strong bond interactions.

Abstract

We obtain the solution of models of self-avoiding walks with attractive interactions on Husimi lattices built with squares. Two attractive interactions are considered: between monomers on first-neighbor sites and not consecutive along a walk and between bonds located on opposite edges of elementary squares. For coordination numbers q>4, two phases, one polymerized the other non-polymerized, are present in the phase diagram. For small values of the attractive interaction the transition between those phases is continuous, but for higher values a first-order transition is found. Both regimes are separated by a tricritical point. For q=4 a richer phase diagram is found, with an additional (dense) polymerized phase, which is stable for for sufficiently strong interactions between bonds. The phase diagram of the model in the three-dimensional parameter space displays surfaces of continuous and discontinuous phase transitions and lines of tricritical points, critical endpoints and triple points.