Exploring the worldline formulation of the Potts model
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.
Cite
@article{arxiv.1911.12728,
title = {Exploring the worldline formulation of the Potts model},
author = {Christof Gattringer and Daniel Göschl and Pascal Törek},
journal= {arXiv preprint arXiv:1911.12728},
year = {2020}
}
Comments
Discussion of statistical errors improved and various comments added. Final version to appear in Nuclear Physics B