Composite operators in Cubic Field Theories and Link Overlap Fluctuations in Spin-Glass Models

TL;DR

This paper characterizes fluctuations of the squared overlap in spin-glass models, revealing distinct critical behaviors for link-overlap fluctuations and specific heat, with implications for cubic field theories.

Contribution

It provides a detailed analysis of composite operators in cubic field theories and their application to spin-glass fluctuations, highlighting new critical behaviors and anomalous logarithmic effects.

Findings

Link-overlap fluctuations are larger than the specific heat.

Link-overlap fluctuations exhibit a subdominant power-law with a logarithmic factor.

Energy-energy correlations have different critical behavior than link-overlap fluctuations.

Abstract

We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field. The analysis reveals that the energy-energy correlations (and thus the specific heat) have a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the $6-\epsilon$ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is missing in the specific heat. In order to compute the $\epsilon$ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.