Orientational ordering in two-dimensional systems with long-range interaction

A variational method for calculating Gaussian fluctuations of two-dimensional (2D) moment orientations in lattice systems with arbitrary anisotropic interaction is proposed. It is asymptotically exact for very low temperatures and gives a good extrapolation for a certain low temperature range. General relationships are obtained that enable one to represent from a unified standpoint and in some cases to refine the known results on: (1) the existence of short-range order in a degenerate 2D system of moments with isotropic short-range interaction, (2) long-range order stabilization by weak local potentials and dipole interactions, (3) the existence of long-range order in a 2D system with interaction of the type V(r)∼|r| ′, if 2< ν <4. For systems with anisotropic long-range dipole interaction of moments on arbitrary 2D lattices (except square ones for which a short-range phase takes place) the existence of long-range order is proved. Lower limits for temperatures of transitions into phases with long-range order are evaluated. The low values of the transition temperatures in the dipole systems can be explained due to the small values of interchain interaction in comparison with interchain ones. The applicability area for the method used is discussed.