Partial ordering at the ground state of frustrated spin-S Ising models

We show that a partial ordering appears in the limit S → ∞ at the ground state of the 1D spin-S antiferromagnetic Ising model with next-nearest-neighbour interaction. This is an analogue of the ordering which appears at finite S = Sc ≈ 3 in the nearest-neighbour Ising antiferromagnet on the triangular lattice. We also show that the ground-state problems.in these spin-S models can be mapped into reweighted S = 12 ground-state problems. Thus the emergence of the order for the model on the triangular lattice is related to the roughening transition in a certain SOS model. For the model on the triangular lattice, the transfer-matrix method is used to calculate the critical exponent η and the central charge c. For 12 ⩽S⩽2, the central charge is almost constant and very close to unity. However, in the rough phase for 2 < S < Sc the central charge slightly deviates from unity, which is in contradiction with some predictions based on the conformal invariance. Explanation of such a deviation which relates the ground-state problem with a certain long-range interacting hard hexagon model is also proposed.