The canonical approach at high temperature revisited

TL;DR

This paper revisits the canonical approach in high-temperature lattice QCD, clarifying a paradox related to the Roberge-Weiss transition and demonstrating its resolution in finite-size systems.

Contribution

It identifies the origin of the paradox in the Roberge-Weiss transition and shows that finite-size effects resolve it, validating the canonical approach for lattice QCD at high temperatures.

Findings

The paradox arises from the Roberge-Weiss transition in infinite systems.

Finite-size effects smear the transition, resolving the paradox.

The canonical approach remains valid in lattice QCD simulations with finite size.

Abstract

This paper discusses a paradox encountered when employing the canonical approach, particularly in the high-temperature region where the Roberge-Weiss transition exists at finite imaginary chemical potential. The paradox is that the results obtained using the canonical approach cannot match the correct results in that region. We show that the paradox originates from the Roberge-Weiss transition in the infinite-size system, which is linked to the non-trivial Polyakov-loop sectors. Furthermore, it is shown that this paradox disappears in finite-size systems because of the smearing effect for the Roberge-Weiss transition, which validates the use of the canonical approach in lattice QCD simulations.