Critical exponents from five-loop scalar theory renormalization near six-dimensions

TL;DR

This paper computes five-loop renormalization constants and critical exponents for scalar cubic interaction models near six dimensions, advancing theoretical understanding of phase transitions in these systems.

Contribution

It provides detailed five-loop calculations of renormalization constants, anomalous dimensions, and critical exponents for scalar and O(n)-symmetric cubic models.

Findings

Five-loop renormalization constants are obtained.

Critical exponents are calculated for scalar and O(n) models.

Methodology allows generalizations to other symmetries.

Abstract

We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants, anomalous dimensions and critical exponents. We discuss in detail the method of calculation, and provide all counterterms up to five loops. This allows one to consider generalizations of the ${\varphi^3}$ theory to other symmetries.