Diagram Reduction in Problem of Critical Dynamics of Ferromagnets: 4-Loop Approximation

TL;DR

This paper introduces a method to significantly reduce the computational complexity of calculating critical exponents in ferromagnetic models using the renormalization group, demonstrated through a 4-loop calculation of the dynamic critical exponent z.

Contribution

The paper presents a novel diagram reduction technique that decreases the number of integrals from 66 to 17 in 4-loop calculations of critical exponents.

Findings

Reduced the number of integrals needed for 4-loop calculations

Successfully computed the critical exponent z at 4-loop level

Demonstrated the effectiveness of Sector Decomposition for numerical estimation

Abstract

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent $z$ of model A at 4-loop level, where our method allows to reduce number of integrals from 66 to 17. The way of constructing the integrand in Feynman representation of such diagrams is discussed. Integrals were estimated numerically with Sector Decomposition technique.