The bimodal Ising spin glass in dimension two : the anomalous dimension $\eta$

TL;DR

This study measures the correlation functions of 2D Gaussian and bimodal Ising spin glasses, revealing a non-zero anomalous dimension for the bimodal case, indicating different universality classes.

Contribution

It provides direct measurements of the correlation function and critical exponents for 2D bimodal and Gaussian Ising spin glasses, highlighting their different universality classes.

Findings

Gaussian case consistent with η=0

Bimodal case has η≈0.28(4) above T*

Bimodal and Gaussian models are in different universality classes

Abstract

Direct measurements of the spin glass correlation function $G(R)$ for Gaussian and bimodal Ising spin glasses in dimension two have been carried out in the temperature region $T \sim 1$. In the Gaussian case the data are consistent with the known anomalous dimension value $\eta \equiv 0$. For the bimodal spin glass in this temperature region $T > T^{*}(L)$, well above the crossover $T^{*}(L)$ to the ground state dominated regime, the effective exponent $\eta$ is clearly non-zero and the data are consistent with the estimate $\eta \sim 0.28(4)$ given by McMillan in 1983 from similar measurements. Measurements of the temperature dependence of the Binder cumulant $U_{4}(T,L)$ and the normalized correlation length $\xi(T,L)/L$ for the two models confirms the conclusion that the 2D bimodal model has a non-zero effective $\eta$ both below and above $T^{*}(L)$. The 2D bimodal and Gaussian interaction distribution Ising spin glasses are not in the same Universality class.