SPIN-WAVE RENORMALIZATION AND THERMALLY-INDUCED ORDER IN 2-DIMENSIONAL DIPOLAR SYSTEMS

In this paper we examine the properties of the planar spin model in tw o dimensions. The spins are assumed to lie on a square lattice and are confined to lie in the plane but are free to rotate within it. It is assumed that the spins interact through the dipolar interaction. The g round state of this model is continuously degenerate, which gives rise to a zero-energy mode in the linearized spin wave spectrum. The prese nce of the zero-energy mode leads to a divergence in the ensemble aver age of the spin wave amplitude. However, it is shown that since the gr ound-state degeneracy does not arise as a consequence of an exact symm etry of the Hamiltonian, but, instead is a peculiarity of the dipolar interaction, the higher-order corrections to the Hamiltonian will indu ce a gap in the spin wave spectra. The appearance of a gap in the reno rmalized spin wave spectra will render the ensemble average of the spi n wave amplitude finite and hence lead to the appearance of long-range magnetic order at low temperature. In this paper we describe a renorm alization scheme that yields a self-consistent description of the low temperature of the properties of this system and provides the basis fo r a low-temperature expansion.