We have shown that the ground-state problem of the spin $S$ antiferromagnetic Ising model on the triangular lattice maps to a certain solid-on-solid (SOS) model. For $S<\mathrm{}{S}_c\sim 3$ this SOS model is in a rough phase while for $S>\mathrm{}{S}_c$ it enters a flat phase. The rough phase, whose stability is examined, corresponds to the critical ground state of the Ising model. We suggest that the flat phase corresponds to the ground state with hidden long-range order.

• Received 22 July 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.3888