Nonuniversal critical behavior of magnetic dipoles on a square lattice

We study the thermal transition between the paramagnetic and antiferromagnetic phases of interacting magnetic dipoles on square lattices in two dimensions. By Monte Carlo simulations, we find strong long-range order in the low temperature phase and a critical behavior that is, as in the fourfold anisotropic XY model, nonuniversal, in that the single-site quadrupolar anisotropy h(4) is a relevant variable. However, the critical indices differ markedly from the ones for the anisotropic XY model. They vary from Ising type, within errors, for h(4)=0, to a critical behavior in the h(4)->infinity limit that is nearly as abrupt as a first-order transition.