A New Field Theoretic Approach to Criticality

TL;DR

This paper introduces a novel field theoretic approach using a reorganized perturbation expansion with a soft propagator to analyze critical behavior, providing convergent series of exponents across dimensions and recovering known results in the limit.

Contribution

It develops a new perturbation expansion method with a soft propagator fixed by covariance, enabling finite approximants and convergent series for critical exponents in various dimensions.

Findings

Finite approximants to the correlation critical exponent are achievable in each order.

A convergent series of exponents is obtained in all spatial dimensions 1 to 3.

The $ ext{epsilon}$-expansion results are recovered as $D$ approaches 3.

Abstract

A reorganized perturbation expansion with a propagator of soft infrared behavior is used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Finite approximants to the correlation critical exponent can be obtained in every order of the modified, soft perturbation expansion. Alternatively, a convergent series of exponents in large orders of the soft perturbation expansion is provided by the renormalization group in all spatial dimensions, $1\leq D\leq3$. The result of the $\epsilon$-expansion is recovered in the $D\rightarrow 3 $ limit.