2-DIMENSIONAL LATTICE MODEL WITH AN INFINITE NUMBER OF ZERO-TEMPERATURE STATES

The two-dimensional Ising model with nearest-neighbor coupling and two second-nearest-neighbor couplings introduced by de Fontaine, Willie, and Moss [Phys. Rev. B 36, 5709 (1987)] is found to have an infinite number of zero-temperature states for any value of concentration between successive vertex points c0 = 1.0, 0.75, 0.50, 0.25, and 0.0. A resolution of the ground states of order by low-temperature expansion is not possible because of the nonconvergence of the series. By analogy to a similar situation in the two-dimensional axial next-nearest-neighbor Ising model, it is conjectured that in the present model the paramagnetic phase persists down to T = 0 with the possibility of floating phases.