Finite Volume Effects in Thermal Field Theory

TL;DR

This paper investigates how finite spatial volume influences thermodynamic quantities in relativistic quantum field theories at zero chemical potential, providing formulas to estimate and correct finite volume effects in lattice QCD thermodynamics.

Contribution

It derives a closed-form expression for leading finite volume effects based on screening masses, aiding more accurate lattice QCD calculations.

Findings

Derived a formula linking finite volume effects to screening masses.

Provided a method to estimate finite volume corrections in lattice simulations.

Enhanced understanding of thermodynamics in finite-sized quantum systems.

Abstract

We analyze the effect of a finite volume on the thermodynamic potentials of a relativistic quantum field theory defined on a hypertorus at vanishing chemical potential. Using the symmetries of the Euclidean partition function, we interpret the thermodynamic observables as the expectation value of the energy-momentum tensor in the same theory living on a $\beta\times L^2$ volume. In the case where the screening correlation lengths in the thermal system are finite, we obtain a closed formula for the leading finite volume effects in terms of the smallest screening mass. This formula can be used to estimate, and possibly correct for, the leading finite volume effects in lattice calculations of QCD thermodynamics.