Planar triangular model with long-range interactions

The effect of dipole and long-range antiferromagnetic isotropic interactions in a triangular planar rotator model is investigated. The ground state is a ferromagnetic (F) configuration for pure dipole interaction and a 120^∘ three-sublattice (T) configuration for pure antiferromagnetic interaction decaying as 1/r³ where r is the spin-spin distance. In between the spins are placed in striped configurations where n rows of spins parallel alternate with n rows of spins antiparallel to a nearest neighbors (NN) direction for any integer n provided that $L/n$ is an even number, L being the lattice size. Monte Carlo simulation confirms the low temperature configurations found by analytic calculation. Specific heat, staggered susceptibility and order parameter are investigated to get the phase diagram and the order of the transition to the paramagnetic phase. The order-disorder phase transition is continuous only for the F phase (pure dipole interaction). It is first order for any nonzero long-range antiferromagnetic exchange interaction.