Magnetic Phase Diagram of the Ising Model on a Triangular Lattice with Antiferromagnetic Nearest-Neighbor and Next-Nearest-Neighbor Interactions

The temperature versus magnetic field phase diagram of the Ising model on a two-dimensional triangular lattice with nearest-neighbor and next-nearest-neighbor interactions is calculated by using the interface method of Müller-Hartmann and Zittartz. Both interactions are assumed to be antiferromagnetic, while the interaction ratio assumes arbitrary positive values. The resulting phase diagrams contain correctly various commensurate phases obtained in the ground state analysis. It is found that no commensurate phase is stable down to zero temperature at certain critical fields. This is explained as a consequence of the geometrical nature of the spin structures of two adjacent commensurate phases. For certain values of the interaction ratio, the phase diagrams are compared favorably with the Monte Carlo results obtained by Saito.