Two-dimensional Ising model with self-dual biaxially correlated disorder

Abstract

We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder, which has a correlator, $G(r)\ensuremath{\sim}{r}^{\ensuremath{-}1}$, represents a relevant perturbation according to the extended Harris criterion. Critical properties of the system are studied by large scale Monte Carlo simulations. The correlation length critical exponent $\ensuremath{\nu}=2.005(5)$ corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density ${x}_{m}=\ensuremath{\beta}∕\ensuremath{\nu}=0.1294(7)$ is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.