Universal sextic effective interaction at criticality

TL;DR

This paper uses advanced renormalization group techniques to accurately estimate the universal critical value of the sextic coupling constant in the three-dimensional Ising model, providing precise numerical results.

Contribution

The paper presents a four-loop RG calculation and resummation methods to determine the universal sextic coupling at criticality, improving previous estimates.

Findings

Estimated g_6^* = 1.596 using Pade-Borel resummation.

Most accurate estimate for g_6^* is 1.61.

Provides refined numerical value for critical sextic coupling.

Abstract

The renormalization group approach in three dimensions is used to estimate the universal critical value g_6^* of the dimensionless sextic effective coupling constant for the Ising model. The four-loop RG expansion for g_6 is calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy procedures resulting in g_6^* = 1.596, while the most accurate estimate for g_6^* is argued to be equal to 1.61.