A renormalization group computation of the critical exponents of hierarchical spin glasses

TL;DR

This paper uses renormalization group techniques to compute critical exponents in hierarchical spin glasses, confirming the theory's validity for non-mean field disordered systems and paving the way for more precise models.

Contribution

It presents a two-loop epsilon-expansion calculation of critical exponents in hierarchical spin glasses using two independent methods, validating the infrared behavior of the theory.

Findings

Both methods agree on the critical exponent value.

The infrared behavior is well-defined in the non-mean field model.

The approach supports developing a predictive non-mean field theory.

Abstract

The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent methods. Both methods yield the same result confirming that the infrared behaviour of the theory if well-defined and the underlying ideas of the Renormalization Group hold also in such non-mean field disordered model. By pushing such calculation to high orders in epsilon, a consistent and predictive non-mean field theory for such disordered system could be established.