Collapse transition of self-avoiding trails on the square lattice

TL;DR

This study confirms that the collapse transition of interacting self-avoiding trails on the square lattice in two dimensions belongs to a different universality class than that of self-avoiding walks, resolving previous simulation discrepancies.

Contribution

The paper demonstrates through large-scale simulations that the collapse transition of interacting self-avoiding trails matches standard models, clarifying their universality class distinction from self-avoiding walks.

Findings

Kinetic growth trail results align with equilibrium models.

Self-avoiding trails and walks have different universality classes.

Large-scale simulations up to 2 million steps support these conclusions.

Abstract

The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails, which map to a particular temperature of interacting self-avoiding trails, showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self-avoiding walks. On the other hand, it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model. In this work we simulate the standard equilibrium interacting self-avoiding trail model on the square lattice up to lengths over $2,000,000$ steps and show that the results of the kinetic growth simulations are, in fact, entirely in accord with standard simulations of the temperature dependent model. In this way we verify that the collapse transition of interacting self-avoiding walks and trails are indeed in different universality classes in two dimensions.