CLASSICAL DIPOLES ON A FINITE TRIANGULAR LATTICE - THE SPHERICAL MODEL APPROXIMATION

In the framework of the spherical model it is shown that a phase transition at finite temperature to a ferromagnetic phase in a two-dimensional system with dipole-dipole and exchange interactions on a lattice with arbitrary rhombicity angle exists if the ferromagnetic ground state is not continuously degenerate in spin direction. When the degeneracy exists, the system exhibits essential singularities in the thermodynamic functions at T = 0. Finite-size effects in such systems are investigated in the example of the triangular latice under periodic boundary conditions. The existence of only one relevant variable determining the crossover from infinite to finite-size behavior is found as T = 0 is approached, despite that there are two characteristic lengths determining the scale of variation of the correlation function. The validity of the general finite-size scalling relations in terms of this variable is established. © 1990.