Critical Behaviour of Magnetic Polymers in Two and Three Dimensions

TL;DR

This paper investigates the critical behavior of magnetic polymers modeled as self-avoiding walks with Ising spins in two and three dimensions, revealing a first-order transition in 3D and a continuous transition in 2D, with estimated critical parameters.

Contribution

It provides the first analysis of magnetic polymer transitions in two dimensions and extends previous three-dimensional studies with new numerical results.

Findings

First-order magnetic and collapse transition in 3D

Continuous transition in 2D

Estimated critical exponents and transition temperature

Abstract

We explore the critical behaviour of two and three dimensional lattice models of polymers in dilute solution where the monomers carry a magnetic moment which interacts ferromagnetically with near-neighbour monomers. Specifically, the model explored consists of a self-avoiding walk on a square or cubic lattice with Ising spins on the visited sites. In three dimensions we confirm and extend previous numerical work, showing clearly the first-order character of both the magnetic transition and polymer collapse, which happen together. We present results for the first time in two dimensions, where the transition is seen to be continuous. Finite-size scaling is used to extract estimates for the critical exponents and transition temperature in the absence of an external magnetic field.