Scheme Independence at First Order Phase Transitions and the Renormalisation Group

TL;DR

This paper investigates how the choice of regularisation scheme affects solutions to the renormalisation group equations in scalar QED, demonstrating universal behavior in strong first-order phase transitions and identifying conditions for bubble nucleation theory.

Contribution

It provides an analysis of scheme dependence in renormalisation group solutions and establishes universality and applicability conditions for phase transition descriptions.

Findings

Physical quantities show universal behavior in strong first-order transitions.

Subleading corrections depend on regularisation scheme but are suppressed at large UV scales.

Derived a condition for the validity of Langer's bubble nucleation theory.

Abstract

We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of scalar QED display universal behaviour for strongly first-order phase transitions. Only subleading corrections depend on the regularisation scheme and are suppressed by a sufficiently large UV scale. We calculate the relevant coarse-graining scale and give a condition for the applicability of Langer's theory of bubble nucleation.