Universality in short-range Ising spin glasses

TL;DR

This paper investigates how the distribution of coupling constants affects the critical behavior of short-range Ising spin glasses, finding universal critical exponents across different initial distributions using real space renormalization group methods.

Contribution

It demonstrates the universality of critical exponents in short-range Ising spin glasses regardless of the initial coupling distribution, using a hierarchical lattice model.

Findings

Critical exponents $eta$ and $ u$ are estimated from local order parameters.

Universal behavior observed across Gaussian, bimodal, uniform, and exponential distributions.

A saddle-point critical point with a fixed-point distribution is identified.

Abstract

The role of the distribution of coupling constants on the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a fixed-point distribution is found in an appropriated parameter space. The critical exponents $\beta $ and $\nu $ are directly estimated from the data of the local Edwards-Anderson order parameters for the model defined on a diamond hierarchical lattice of fractal dimension $d_{f}=3$. Four distinct initial distributions of coupling constants (Gaussian, bimodal, uniform and exponential) are considered; the results clearly indicate a universal behavior.