Solution of the sign problem in the Potts model at fixed fermion number

TL;DR

This paper demonstrates how a cluster algorithm can solve the sign problem in a 3-state Potts model approximation of finite-density QCD, enabling accurate calculations in previously challenging regimes.

Contribution

It introduces a cluster algorithm that averages over Z(3) sectors to eliminate the sign problem in the Potts model at finite fermion density.

Findings

Sign problem is resolved using cluster averaging over Z(3) sectors.

Improved estimators account for cluster triality, enhancing physical quantity calculations.

Method extends to regimes beyond strong coupling where sign problem persists.

Abstract

We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a 3-state Potts model. In the strong coupling limit, the model is free of the sign problem. Away from the strong coupling, the sign problem is solved by employing a cluster algorithm which allows to average each cluster over the Z(3) sectors. Improved estimators for physical quantities can be constructed by taking into account the triality of the clusters, that is, their transformation properties with respect to Z(3) transformations.