Phase transitions in systems of magnetic dipoles on a square lattice with quenched disorder

We study by Monte Carlo simulations the effect of quenched orientational disorder in systems of interacting classical dipoles on a square lattice. Each dipole can lie along any of the two perpendicular axes that form an angle ψ with the principal axes of the lattice. We choose ψ at random and without bias from the interval [-Δ,Δ] for each site of the lattice. For 0≤Δ≤π/4 we find a thermally driven second order transition between a paramagnetic and a dipolar antiferromagnetic order phase and critical exponents that change continuously with Δ. Near the case of maximum disorder Δ∼π/4 we still find a second order transition at a finite temperature Tc but our results point to weak instead of strong long-ranged dipolar order for temperatures below Tc.