Critical Behaviour of 3D Systems with Long-Range Correlated Quenched Defects

TL;DR

This paper investigates the critical behavior of three-dimensional systems with long-range correlated quenched defects, using a field-theoretic approach and two-loop renormalization analysis to identify stable fixed points and compute critical exponents.

Contribution

It provides a novel two-loop renormalization analysis for 3D systems with power-law correlated quenched defects, differing from previous epsilon-delta expansion results.

Findings

Identification of stable fixed points for various correlation parameters

Calculation of critical exponents using Pade-Borel summation

Demonstration of differences from earlier epsilon-delta expansion results

Abstract

A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations $\sim |{\bf x}|^{-a}$ for large separations ${\bf x}$ is given. Directly for three-dimensional systems and different values of correlation parameter $2\leq a \leq 3$ a renormalization analysis of scaling function in the two-loop approximation is carried out, and the fixed points corresponding to stability of the various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by double $\epsilon, \delta$ - expansion. The critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.