The Canonical Approach at High Temperature Revisited

This study examines an apparent discrepancy that can arise between the canonical construction and the Taylor expansion constructed from a high-temperature thermodynamic potential restricted to the trivial Polyakov-loop sector in the presence of the Roberge–Weiss transition. We show that the discrepancy originates from the distinction between the full Roberge–Weiss-periodic partition function and a representation restricted to a single Polyakov-loop sector. We further discuss how this distinction is affected by the thermodynamic limit and why it does not cause a problem for the standard finite-volume canonical formulation used in lattice QCD simulations. We also discuss how to connect the full RW-periodic partition function with a single-sector expression in the thermodynamic limit.