Universality of collapsing two-dimensional self-avoiding trails

TL;DR

This paper demonstrates through numerical transfer matrix calculations that two-dimensional self-avoiding trails at the collapse transition belong to the same universality class as the O(n=0) model, challenging prior assumptions.

Contribution

It provides the first numerical evidence that self-avoiding trails share universality with the O(n=0) model at collapse, revising previous conjectures.

Findings

Self-avoiding trails at collapse have thermal exponent 12/23.

They belong to the same universality class as the O(n=0) model.

Results challenge earlier beliefs about their universality class.

Abstract

Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same universality class as the O(n=0) model of Blote and Nienhuis (or vertex-interacting self-avoiding walk), which has thermal exponent $\nu=12/23$, contrary to previous conjectures.