Computer-simulation study of a disordered plane-rotator system in two dimensions with long-range ferromagnetic interactions

We consider a classical system, consisting of two-component unit vectors {uₖ}, associated with a square lattice, and interacting via translationally and rotationally invariant pair potentials of the long-range and ferromagnetic form W=Wⱼₖ=-{ε}{}xⱼ-xₖ{{{}}}^{{{-}}p}uⱼ{·}uₖ, {ε}>0, p>2, where xₖ are the coordinates of the lattice sites. Combining available theoretical results, one can conclude that for all p{≥}4 the system disorders at all finite temperatures and exhibits a transition to a low-temperature phase with infinite susceptibility (Kosterlitz-Thouless-like transition); theoretical bounds on the transition temperature can also be obtained. We report here Monte Carlo simulation results for the potential model defined by p=4 and estimate its transition temperature to be Tc,4*=2.23±{}0.03, where T*=kBT/{ε}.