Functional renormalisation group in a finite volume

TL;DR

This paper investigates a $$-theory at finite temperature and volume using the functional renormalisation group, analyzing how thermodynamical quantities approach their infinite-volume limits and improving the method's applicability.

Contribution

It advances the functional renormalisation group technique for finite volume systems and identifies regulator conditions for exponential decay properties.

Findings

Thermodynamical observables approach the infinite volume limit similarly to the zero-temperature case.

The method is refined with regulator conditions that ensure exponential decay in thermal and volume fluctuations.

Finite volume effects on pressure and other thermodynamic quantities are quantitatively characterized.

Abstract

We study a $\phi^4$-theory at finite temperature in a finite volume. Quantum, thermal and volume fluctuations are treated with the functional renormalisation group. Specifically, we focus on the interplay of temperature and length scales driving the system. We find that thermodynamical observables at finite volume such as the pressure approach the infinite volume limit similarly to that of the vanishing temperature limit. We also advance the functional renormalisation group method at finite volume. In particular, we identify requirements for suitable regulators that admit the exponential thermal and finite volume decay properties.