Spatial correlation functions in 3-d Ising spin glasses

TL;DR

This paper studies the behavior of spin-spin correlation functions in 3D Ising spin glasses, combining theoretical replica field analysis with numerical simulations to understand the nature of the longitudinal mode at different length scales.

Contribution

It provides a detailed analysis of the infrared behavior of correlation functions and identifies the longitudinal mode as massive at certain length scales in 3D Ising spin glasses.

Findings

Longitudinal mode behaves as massive at intermediate scales

Numerical data supports exponential decay of correlations

Analysis aligns with replica field theory predictions

Abstract

We investigate spin-spin correlation functions in the low temperature phase of spin-glasses. Using the replica field theory formalism, we examine in detail their infrared (long distance) behavior. In particular we identify a longitudinal mode that behaves as massive at intermediate length scales (near-infrared region). These issues are then addressed by numerical simulation; the analysis of our data is compatible with the prediction that the longitudinal mode appears as massive, i.e., that it undergoes an exponential decay, for distances smaller than an appropriate correlation length.