Field-Theoretic Techniques in the Study of Critical Phenomena

TL;DR

This paper discusses the application of field-theoretic methods within Wilson's renormalization framework to understand critical phenomena, and proposes Borel summability of certain renormalization functions in scalar theories.

Contribution

It clarifies the role of field-theoretic techniques in Wilson's renormalization and suggests Borel summability of beta-functions in minimal subtraction schemes.

Findings

Field-theoretic approach aligns with Wilson's renormalization theory.

Beta-functions in scalar theories may be Borel summable.

Qualitative discussion on the validity domain of the approach.

Abstract

We shortly illustrate how the field-theoretic approach to critical phenomena takes place in the more complete Wilson theory of renormalization and qualitatively discuss its domain of validity. By the way, we suggest that the differential renormalization functions (like the beta-function) of the perturbative scalar theory in four dimensions should be Borel summable provided they are calculated within a minimal subtraction scheme.