Short Range Ising Spin Glasses: a critical exponent study

TL;DR

This study investigates the critical exponents of short-range Ising spin-glass models on hierarchical lattices with varying fractal dimensions, revealing deviations from universality across different initial coupling distributions.

Contribution

It provides a detailed analysis of critical exponents using a Migdal-Kadanoff renormalization approach on fractal lattices, considering multiple initial distributions.

Findings

Critical exponents estimated for different fractal dimensions.

Deviations from universal behavior observed across distributions.

Analysis of renormalized flow explains non-universality.

Abstract

The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent $\beta $ is directly estimated from the data of the local Edwards- Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the $\nu $ exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space.