Critical behavior of the 2D Ising model with long-range correlated disorder

Abstract

We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $\sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $\nu =2/a+O((2-a{)}^3)$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\eta }_2=1/2-(2-a)/4+O((2-a{)}^2)$.

14 pages, 3 figures, revtex4

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• Infinite disorder and correlation fixed point in the Potts model with correlated disorder
• Critical exponent $\nu$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
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• Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder
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• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects