Interacting self-avoiding polygons

TL;DR

This paper analyzes a model of interacting self-avoiding polygons, deriving the critical conditions for phase transitions and characterizing regimes of space-filling behavior and bounded exponential moments.

Contribution

It provides an exact computation of the critical curve and characterizes different phases of the interacting polygons system.

Findings

Identified the critical curve separating long and localized polygons.

Proved existence of a space-filling regime.

Characterized the regime with bounded exponential moments.

Abstract

We consider a system of self-avoiding polygons interacting through a potential that penalizes or rewards the number of mutual touchings and we provide an exact computation of the critical curve separating a regime of long polygons from a regime of localized polygons. Moreover, we prove the existence of a sub-region of the phase diagram where the self-avoiding polygons are space filling and we provide a non-trivial characterization of the regime where the polygon length admits uniformly bounded exponential moments.