Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipola r forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles alpha , -alpha, pi+alpha, pi-alpha with a reference axis, alpha being arbitrary. This infinite degeneracy of the ground state is accidental in nature and on e expects that it is removed by thermal fluctuations in agreement with Mont e Carlo simulation. Indeed we find that the elementary excitation energies which depend on alpha lead to a free energy which is a function of alpha wi th minima at alpha = 0 and alpha = pi/2 corresponding to columnar configura tions. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder.