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

TL;DR

This paper investigates the critical behavior of the 2D Ising model with algebraically decaying long-range correlated disorder, identifying a stable non-trivial fixed point and calculating associated critical exponents.

Contribution

It introduces a detailed renormalization group analysis of the 2D Ising model with correlated disorder, revealing a new stable fixed point and deriving critical exponents.

Findings

Existence of a stable non-trivial fixed point for 0.995<a<2

Critical exponent for correlation length: ν=2/a + corrections

Critical exponent for spin-spin correlations: η_2=1/2-(2-a)/4+ corrections

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 $\eta_2=1/2-(2-a)/4+O((2-a)^2)$.