Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder

TL;DR

This study explores how long-range correlated disorder affects the ordering in the 2D Ising spin glass, finding that such correlations do not induce finite-temperature order but influence local domain structures.

Contribution

It provides a numerical analysis showing that long-range bond correlations do not produce spin-glass order at finite temperature in 2D, but significantly affect local magnetic domains.

Findings

Bond correlations do not lead to finite-temperature spin-glass order.

Correlations induce ferro/antiferromagnetic domains at local scales.

The domain length scale diverges as the correlation exponent approaches zero.

Abstract

The standard two-dimensional Ising spin glass does not exhibit an ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as $(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground state and domain wall excitations. Our results indicate that the inclusion of bond correlations does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro/antiferromagnetic domains into the system. The length scale of ferro/antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, $a \to a_c = 0$. Thus, our results suggest that the system becomes a ferro/antiferromagnet only in the limit $a \to 0$.