Critical dynamics and effective exponents of magnets with extended impurities

TL;DR

This paper studies the critical behavior of three-dimensional magnets with extended, correlated impurities, using advanced resummation techniques to accurately determine static and dynamic critical exponents.

Contribution

It applies Chisholm-Borel resummation to two-loop expansions to reliably compute critical exponents for magnets with extended defects, advancing understanding of their effective critical behavior.

Findings

Numerical values for asymptotic critical exponents obtained.

Different scenarios for static and dynamic effective critical behavior discussed.

Non-universal exponents for various defect configurations provided.

Abstract

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.