Fluctuation-induced transitions in an isotropic spatially frustrated lattice model

In this paper we discuss the effects of fluctuations on the phase diagram of an isotropic Ising model with ferromagnetic first-neighbor and antiferromagnetic second- and third-neighbor interactions. We find that, in certain cases, there are substantial deviations from mean-field behavior. Thus the phase transitions between the one-dimensional modulated phases and paramagnetic phase are found to undergo fluctuation-induced first-order phase transitions. We also discuss that point of the phase diagram which, within mean-field theory, was predicted to be an isotropic Lifshitz point. It is argued that the existence of such a point is unlikely, and some alternative scenarios are proposed.