Nearest-neighbor Ising model with a uniaxial incommensurate phase and a Lifshitz point

Abstract

The anisotropic triangular nearest-neighbor Ising model, with antiferromagnetic interactions, is studied. The phase diagram, as a function of temperature and field, has a complex structure. Two commensurate ordered phases are found. The transition to one is Ising-type. The second is reached from the disordered phase in one of two ways: either via an intermediate uniaxial incommensurate phase---which is reached at high temperatures by a Kosterlitz-Thouless transition and at low temperatures undergoes an incommensurate-commensurate transition---or by a single continuous transition. The latter transition is in the same universality class as the chiral three-state Potts model, with thermal exponent within 4% of that of the three-state Potts model. These two transition regimes are found to be separated by a Lifshitz point. The phase diagram and critical behavior were determined by analytical (symmetry analysis and free-fermion approximation) as well as numerical (phenomenological renormalization-group and Monte Carlo) methods.