Critical behavior of the 2D Ising model with long-range correlated   disorder
  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 $\eta_2=1/2-(2-a)/4+O((2-a)^2)$. 
Maxym Dudka, Andrei A. Fedorenko, Viktoria Blavatska, Yurij Holovatch
cond-mat.dis-nn cond-mat.stat-mech