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

Abstract

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 = S c ≈ 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 = 1 2 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 1 2 ⩽S⩽2 , the central charge is almost constant and very close to unity. However, in the rough phase for 2 < S < S c 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.