XY model on a self-avoiding walk

TL;DR

This paper investigates a magnetic polymer model with XY spins on a self-avoiding walk, revealing continuous phase transitions in 2D and first-order in 3D through Monte Carlo simulations.

Contribution

It introduces a dynamic lattice XY model on self-avoiding walks and characterizes its phase transitions near the theta-point.

Findings

Transitions are continuous in 2D.

Transitions are first-order in 3D.

Transitions resemble those in Ising spin models.

Abstract

We study a lattice model of a magnetic polymer where the XY spin variables are located on a self-avoiding walk (SAW) on a regular lattice in two and three dimensions. We consider the regime where both spins and conformations are dynamic, thus the XY model is defined on a dynamic lattice and conformations generate an annealed disorder. Using Monte Carlo simulations, we characterize the globule-coil and ferromagnetic phase transitions, and pay special attention to the vicinity of the theta-point. Our numerical results suggest that the transitions are continuous in two dimensions and first-order in three dimensions, which is similar to related models with Ising spins.