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

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 $a\to 0$.

arXiv comment10 pages, 10 figures

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• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Replica-symmetry breaking for directed polymers
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• Exact mapping of a spin glass with correlated disorder to the pure Ising model