Analytical Solutions of Exact Renormalization Group Equations

TL;DR

This paper derives analytical solutions to exact renormalization group equations, revealing diverse physical phenomena like phase transitions, fixed points, and critical behavior in various models.

Contribution

It provides the first set of analytical solutions for the scale dependence of potentials in the effective average action framework.

Findings

Identification of fixed points and their role in phase transitions

Analytical expressions for critical exponents

Demonstration of radiatively induced first order transitions

Abstract

We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions, critical exponents, first order transitions (some of which are radiatively induced) and tricritical behaviour.