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.

中文翻译：

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探索Potts模型的世界线表述

我们将重新讨论q- state Potts模型的世界线公式化问题，并讨论任意尺寸的世界线表示形式，该形式也允许使用磁性项。对于消失的磁场，我们实现了Hodge分解来解决具有双变量的约束，这在二维上意味着自对偶性是一个简单的推论。我们基于蠕虫算法，根据世界线提出了探索性的二维蒙特卡罗模拟。我们既研究，消失和非零磁场，并探讨q之间$q=2$ 和 $q=30$，即具有连续以及强一阶跃迁的Potts模型。