Roughening transitions and the zero-temperature triangular Ising antiferromagnet

Abstract

The zero-temperature triangular Ising antiferromagnet is mapped onto a solid-on-solid (SOS) model. The system undergoes a roughening transition characterised by a critical exponent alpha =¹/₂, by the absence of excitations in the smooth phase, and by domain wall excitations (stripes) in the rough phase. At infinite SOS temperature the height-height correlation function is explicitly calculated with the aid of known four-point Ising correlations. The authors point out that a certain six-vertex model with a comparable SOS interpretation has an identical critical temperature, critical exponent and critical amplitude. This is in support of existing ideas on university in systems with striped phases.