Critical behavior of disordered systems with replica symmetry breaking

TL;DR

This paper investigates the critical behavior of weakly disordered systems with multiple components, using advanced field-theoretic and renormalization group techniques to analyze replica symmetry breaking effects across different dimensions.

Contribution

It provides a detailed two-loop renormalization group analysis of disordered systems with replica symmetry breaking, including fixed point determination and critical behavior classification.

Findings

Fixed points for one-step replica symmetry breaking identified.

Threshold dimensions for different critical behaviors determined.

Comparison with epsilon-expansion results enhances understanding of method applicability.

Abstract

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $\epsilon$-expansion and the scope of the method applicability is determined.