Order parameter for non-mean-field spin glasses

TL;DR

This paper introduces a new renormalization group method for non-mean-field spin glasses that reveals a novel order parameter emerging from system symmetries, improving understanding of critical behavior.

Contribution

A minimality principle-based RG approach that uncovers a spontaneous order parameter in non-mean-field spin glasses without prior assumptions.

Findings

Order parameter emerges from system symmetries and self-similarity.

Predictions for critical exponent ν align with numerical simulations.

Method applicable to realistic spin-glass materials and models.

Abstract

We propose a novel renormalization group (RG) method for non mean-field models of spin glasses, which leads to the emergence of a novel order parameter. Unlike previous approaches where the RG procedure is based on a priori notions on the system, our analysis follows a minimality principle, where no a priori assumption is made. We apply our approach to a spin-glass model built on a hierarchical lattice. In the RG decimation procedure, a novel order parameter spontaneously emerges from the system symmetries, and self-similarity features of the RG transformation only. This order parameter is the projection of the spin configurations on the ground state of the system. Kadanoff's majority rule for ferromagnetic systems is replaced by a more complex scheme, which involves such novel order parameter. The ground state thus acts as a pattern which translates spin configurations from one length scale to another. The rescaling RG procedure is based on a minimal, information-theory approach and, combined with the decimation, it yields a complete RG transformation. Below the upper critical dimension, the predictions for the critical exponent $\nu$, which describes the critical divergence of the correlation length, are in excellent agreement with numerical simulations from both this and previous studies. Overall, this study opens new avenues in the understanding of the critical ordering of realistic spin glasses, and it can be applied to spin-glass models on a cubic lattice and nearest-neighbor couplings which directly model spin-glass materials, such as AuFe, CuMn and other magnetic alloys.