Exploring the worldline formulation of the Potts model

TL;DR

This paper develops a worldline formulation for the q-state Potts model in arbitrary dimensions, enabling efficient Monte Carlo simulations and analysis of phase transitions with magnetic fields.

Contribution

It introduces a novel worldline representation for the Potts model that incorporates magnetic terms and applies dual variables, extending previous formulations.

Findings

Successful implementation of worm algorithms for 2D simulations

Analysis of phase transitions for q between 2 and 30

Demonstration of self-duality in two dimensions

Abstract

We revisit the issue of worldline formulations for the q-state Potts model and discuss a worldline representation in arbitrary dimensions which also allows for magnetic terms. For vanishing magnetic field we implement a Hodge decomposition for resolving the constraints with dual variables, which in two dimensions implies self-duality as a simple corollary. We present exploratory 2-d Monte Carlo simulations in terms of the worldlines, based on worm algorithms. We study both, vanishing and non-zero magnetic field, and explore q between q = 2 and q = 30, i.e., Potts models with continuous, as well as strong first order transitions.