Generalized cluster algorithms for Potts lattice gauge theory

Anthony E. Pizzimenti; Paul Duncan; Benjamin Schweinhart

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arXiv · 2507.13503

Generalized cluster algorithms for Potts lattice gauge theory

Anthony E. Pizzimenti·Paul Duncan·Benjamin Schweinhart

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Abstract

Monte Carlo algorithms, like the Swendsen-Wang and invaded-cluster, sample the Ising and Potts models asymptotically faster than single-spin Glauber dynamics do. Here, we generalize both algorithms to sample Potts lattice gauge theory by way of a $2$-dimensional cellular representation called the plaquette random-cluster model. The invaded-cluster algorithm targets Potts lattice gauge theory at criticality by implementing a stopping condition defined in terms of homological percolation, the emergence of spanning surfaces on the torus. Simulations for $\mathbb Z(2)$ and $\mathbb Z(3)$ lattice gauge theories on the cubical $4$-dimensional torus indicate that both generalized algorithms exhibit much faster autocorrelation decay than single-spin dynamics and allow for efficient sampling on $4$-dimensional tori of linear scale at least $40$.

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cond-mat.stat-mech cs.CG math-ph math.MP math.PR

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BibTeX RIS

Anthony E. Pizzimenti, Paul Duncan, Benjamin Schweinhart. 2025-07-17. Generalized cluster algorithms for Potts lattice gauge theory. https://arxiv.org/abs/2507.13503

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