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 ψψ with the principal axes of the lattice. We choose ψψ at random and without bias from the interval [-Δ,Δ][-Δ,Δ] for each site of the lattice. For 0⩽Δ≲π/40⩽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 ΔΔ. Near the case of maximum disorder Δ≈π/4Δ≈π/4 we still find a second order transition at a finite temperature TcTc but our results point to weak instead of strong   long-ranged dipolar order for temperatures below TcTc.