Two-dimensional ising model with competing interactions : floating phase, walls and dislocations

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Abstract
A two-dimensional, anisotropic Ising model with competing interactions (Selke's « ANNNI» model) is studied by analytic methods. As a first approximation the system is described as a sequence of infinite stripes of positive and negative spins separated by « walls ». The phase diagram exhibits three phases : the ferromagnetic phase, a phase with two « up » layers followed by two « down » layers, and so on, and a « floating » phase with continuously varying wave vector. If dislocations of the wall array are taken into account an additional, paramagnetic phase appears. The paramagnetic phase is argued to extend down to zero temperature in disagreement with results deduced from computer simulations by Selke and Fisher. The present results are in strong contrast with those obtained in the corresponding three-dimensional model which exhibits an infinity of locked, commensurate phases