Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet

TL;DR

This paper investigates how replica symmetry breaking affects the critical behavior of weakly disordered ferromagnets, revealing instability of traditional RG flows and suggesting a new spin glass type criticality near the transition temperature.

Contribution

It extends the renormalization group analysis to include RSB effects, showing the instability of fixed points and the emergence of strong coupling regimes in disordered ferromagnets.

Findings

Traditional RG flows are unstable with respect to RSB potentials.

No stable fixed points exist for general RSB structures.

RG flows lead to strong coupling regimes at finite scales.

Abstract

We study the critical properties of the weakly disordered $p$-component ferromagnet in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects coming from the multiple local minima solutions of the mean-field equations. It is shown that for $p < 4$ the traditional RG flows at dimensions $D=4-\epsilon$, which are usually considered as describing the disorder-induced universal critical behavior, are unstable with respect to the RSB potentials as found in spin glasses. It is demonstrated that for a general type of the Parisi RSB structures there exists no stable fixed points, and the RG flows lead to the {\it strong coupling regime} at the finite scale $R_{*} \sim \exp(1/u)$, where $u$ is the small parameter describing the disorder. The physical concequences of the obtained RG solutions are discussed. In particular, we argue, that discovered RSB strong coupling phenomena indicate on the onset of a new spin glass type critical behaviour in the temperature interval $\tau < \tau_{*} \sim \exp(-1/u)$ near $T_{c}$. Possible relevance of the considered RSB effects for the Griffith phase is also discussed.