Exact renormalization group equations and the field theoretical approach to critical phenomena

TL;DR

This paper discusses the exact renormalization group equations and their relation to the field theoretical approach in understanding critical phenomena, highlighting concepts like continuum limit, renormalizability, and series singularities.

Contribution

It bridges the perturbative field theoretical approach with the nonperturbative Wilson approach to critical phenomena, clarifying their connections.

Findings

Relation between perturbative and nonperturbative approaches clarified

Discussion on singularities in perturbative series

Insights into continuum limit and renormalizability

Abstract

After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the presence of singularities in the perturbative series are discussed.