Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model.

Damien Foster,Claire Pinettes,Ralph Kenna

doi:10.3390/e21020153

Abstract

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, and , are estimated from the scaling behavior of the leading partition function zeros.

Highlights

The interacting self-avoiding walk (ISAW) is the canonical lattice model for a polymer in dilute solution, which takes solvent quality into account [1,2]
The arguments that led to the ISAW model are quite general and are satisfied by other models, in particular, the interacting self-avoiding trail (ISAT) model [4] and the vertex-interacting self-avoiding walk (VISAW) model (which corresponds to the n → 0 limit of an O(n) model proposed by Blöte and Nienhuis) [5]
The difference between the two models is that the ISAT walk is allowed to cross at a site while the VISAW is not

Summary

Introduction

The interacting self-avoiding walk (ISAW) is the canonical lattice model for a polymer in dilute solution, which takes solvent quality into account [1,2]. The arguments that led to the ISAW model are quite general (an excluded volume interaction and short-ranged attraction) and are satisfied by other models, in particular, the interacting self-avoiding trail (ISAT) model [4] and the vertex-interacting self-avoiding walk (VISAW) model (which corresponds to the n → 0 limit of an O(n) model proposed by Blöte and Nienhuis) [5]. In both models the self-avoidance is modelled at the level of the lattice bonds (the walk is only allowed to visit a lattice bond once).

Methods

Results

Conclusion