The Stefan-Boltzmann law in a small box and the pressure deficit in hot SU(N) lattice gauge theory

TL;DR

This paper examines finite-size effects on blackbody radiation in a small box and their implications for the pressure deficit in hot SU(N) lattice gauge theory, providing a closed-form expression for thermodynamic modifications.

Contribution

It derives a closed-form expression for finite-size effects on thermodynamic functions in a small box, linking these effects to pressure deficits in lattice gauge theory simulations.

Findings

Finite-size effects cause about 5% deviation in free energy density at LT~4.

Finite-size effects may explain nearly half of the pressure deficit observed at T~4 T_c.

The results connect finite-volume corrections to lattice simulation discrepancies.

Abstract

The blackbody radiation in a box L^3 with periodic boundary conditions in thermal equilibrium at a temperature T is affected by finite-size effects. These bring about modifications of the thermodynamic functions which can be expressed in a closed form in terms of the dimensionless parameter LT. For instance, when LT~4 - corresponding to the value where the most reliable SU(N) gauge lattice simulations have been performed above the deconfining temperature T_c - the deviation of the free energy density from its thermodynamic limit is about 5%. This may account for almost half of the pressure deficit observed in lattice simulations at T~ 4 T_c.