The phase diagram of a system of classical spins on a square lattice, interacting through a nearest-neighbor antiferromagnetic exchange and a dipolar interaction, is presented. The phase diagram is based on results from a series of Monte Carlo simulations. The phase diagram shows a parallel antiferromagnetic phase, in which the spins are aligned in the x-y plane, and an antiferromagnetic perpendicular phase, in which the spins are aligned perpendicular to the x-y plane. The critical value of the exchange interaction, J c (T), on the phase boundary separating the two phases shows only a weak dependence on temperature (J c ϷJ 0 ), while the transition appears to be first order with an extremely small latent heat. The Monte Carlo data also indicate that the parallel phase separates into two distinct phases, although further work is required to determine the precise nature of the phase boundary separating the two regions. Finally, the low-temperature magnetization data suggest a softening of the spin-wave stiffness close to the phase boundary. The Néel temperature of the perpendicular antiferromagnetic phase is found to be consistent with earlier predictions of spin-wave calculations.

The phase diagram of an ultrathin film of magnetic rotors confined to the plane of the film has been determined from Monte Carlo simulations. In this square lattice system, the classical spins interact through a nearest neighbour antiferromagnetic exchange and the dipolar interactions. The phase diagram shows a dipolar antiferromagnetic phase for low values of |J |/g, and a simple antiferromagnetic phase for large values of |J |/g. The Monte Carlo data also indicate that the dipolar phase separates into two distinct phases for different values of |J |/g. In the first phase the spins are aligned along the x-or y-axis, while in the second phase the sublattice magnetization is oriented at π/4 to the xand y-axis. The results for the plane rotator model are compared with previous results obtained for the Heisenberg model, which showed an analogous phase behaviour. This comparison clarifies the role played by out-of-plane degree of freedom and provides some further insight into this intriguing transition.

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The results from a series of Monte Carlo simulations are presented for the twodimensional Heisenberg model consisting of classical spin vectors arranged on the vertices of a square lattice in which the spins interact through an antiferromagnetic exchange interaction, a magnetic surface anisotropy and the dipolar interaction. The simulations focus on the exchange dominated regime in which the strength of the exchange interaction is significantly greater than both the dipolar interaction and the magnetic surface anisotropy. The results from the simulations show that there exists a range of the magnetic surface anisotropy parameter values in which the system exhibits a reorientation transition from a planar antiferromagnetic phase at low temperature to a perpendicular antiferromagnetic phase at higher temperature. The phase diagram, obtained from the Monte Carlo calculations, is determined as a function of both temperature and magnetic surface anisotropy parameter for a fixed value of the exchange constant. In addition, the low temperature magnetization data suggests a softening of a spin wave stiffness close to the phase boundary between the two ordered states.

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