  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 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,
\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=0.1294(7), is somewhat larger than in the pure
system. Conformal properties of the magnetization and energy density profiles
are also examined numerically.
