Critical behavior of magnetic systems with extended impurities in general dimensions

TL;DR

This paper studies the critical behavior of magnetic systems with extended, correlated impurities across various dimensions using renormalization group techniques and resummation methods.

Contribution

It provides a detailed analysis of critical properties in systems with extended defects, including numerical critical exponents for different dimensions.

Findings

Critical exponents calculated for various dimensions and defect correlations.

Application of two-loop RG functions and Chisholm-Borel resummation.

Insights into universality classes with extended impurities.

Abstract

We investigate the critical properties of d-dimensional magnetic systems 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; both in the case of fixed dimension d=3 and when the space dimension continuously changes from the lower critical dimension to the upper one. The renormalization group calculations are performed in the minimal subtraction scheme. We analyze the two-loop renormalization group functions for different fixed values of the parameters $d, \epsilon_d$. To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the universality class of this system.