Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study

TL;DR

This study uses functional renormalization group methods to analyze the critical behavior of O(N) models with long-range correlated random fields and anisotropies, revealing new fixed points, phase diagrams, and critical exponents.

Contribution

It introduces a double epsilon and sigma expansion to analyze long-range disorder effects, highlighting limitations of previous finite-coupling RG approaches.

Findings

Long-range disorder correlator remains analytic.

Short-range disorder develops a cusp in the correlator.

Phase diagrams and critical exponents are computed for various parameters.

Abstract

We study the long-distance behavior of the O(N) model in the presence of random fields and random anisotropies correlated as ~1/x^{d-sigma} for large separation x using the functional renormalization group. We compute the fixed points and analyze their regions of stability within a double epsilon=d-4 and sigma expansion. We find that the long-range disorder correlator remains analytic but generates short-range disorder whose correlator develops the usual cusp. This allows us to obtain the phase diagrams in (d,sigma,N) parameter space and compute the critical exponents to first order in epsilon and sigma. We show that the standard renormalization group methods with a finite number of couplings used in previous studies of systems with long-range correlated random fields fail to capture all critical properties. We argue that our results may be relevant to the behavior of He-3A in aerogel.