The role of three-body interactions in two-dimensional polymer collapse

TL;DR

This study uses Monte Carlo simulations to explore how three-body interactions influence the collapse transition of two-dimensional polymers, revealing a phase diagram with regions of different critical behaviors, including first-order and $ heta$-point classes.

Contribution

It introduces a generalized model with explicit three-body interactions and maps the phase diagram, identifying conditions for different collapse transition types in 2D polymers.

Findings

Both models exhibit similar phase diagrams with regions of first-order and $ heta$-point collapse.

Three-body interactions can induce a first-order collapse transition.

A higher order critical point likely separates different collapse regimes.

Abstract

Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the Duplantier-Saleur $\theta$-point university class (specific heat cusp), the interacting trail class (specific heat divergence) or even first-order. Here we study via Monte Carlo simulation a generalisation of the Duplantier-Saleur model on the honeycomb lattice and also a generalisation of the so-called vertex-interacting self-avoiding walk model (configurations are actually restricted trails known as grooves) on the triangular lattice. Crucially for both models we have three and two body interactions explicitly and differentially weighted. We show that both models have similar phase diagrams when considered in these larger two-parameter spaces. They demonstrate regions for which the collapse transition is first-order for high three body interactions and regions where the collapse is in the Duplantier-Saleur $\theta$-point university class. We conjecture a higher order multiple critical point separating these two types of collapse.