Self-avoiding trails with nearest neighbour interactions on the square lattice

TL;DR

This study investigates whether the type of attractive interaction influences the universality class of polymer collapse transitions by simulating a new self-avoiding trail model with nearest-neighbour interactions.

Contribution

The paper introduces and analyzes a self-avoiding trail model with nearest-neighbour attraction to identify the source of universality class differences in polymer collapse transitions.

Findings

Collapse transition in INNSAT resembles ISAW universality class

Type of attractive interaction influences universality class

Simulation results support interaction type as key factor

Abstract

Self-avoiding walks and self-avoiding trails, two models of a polymer coil in dilute solution, have been shown to be governed by the same universality class. On the other hand, self-avoiding walks interacting via nearest-neighbour contacts (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the coil-globule, or collapse transition of a polymer in dilute solution. On the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class. The models differ in two substantial ways. They differ in the types of subsets of random walk configurations utilised (site self-avoidance versus bond self-avoidance) and in the type of attractive interaction. It is therefore of some interest to consider self-avoiding trails interacting via nearest neighbour attraction (INNSAT) in order to ascertain the source for the difference in the collapse universality class. Using the flatPERM algorithm, we have performed computer simulations of this model. We present numerical evidence that the singularity in the free energy of INNSAT at the collapse transition has a similar exponent to that of the ISAW model rather than the ISAT model. This would indicate that the type of interaction used in ISAW and ISAT is the source of the difference in universality class.