Renormalization-group description of nonequilibrium critical short-time relaxation processes: a three-loop approximation

TL;DR

This paper develops a three-loop renormalization group approach to analyze how nonequilibrium initial conditions affect the early-time critical relaxation of systems with an n-component order parameter, providing precise numerical estimates.

Contribution

It introduces a three-loop approximation within a renormalization group framework to calculate the dynamic critical exponent for nonequilibrium short-time relaxation.

Findings

Calculated the dynamic critical exponent $ heta'$ for three-dimensional systems.

Used $ ext{ε}$-expansion and Padé-Borel summation methods.

Provided numerical values for $ heta'$ relevant to critical dynamics.

Abstract

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent $\theta'$ of the short time evolution of a system with an $n$-component order parameter is calculated within a dynamical dissipative model using the method of $\varepsilon$-expansion in a three-loop approximation. Numerical values of $\theta'$ for three-dimensional systems are determined using the Pad\'{e}-Borel method for the summation of asymptotic series.