Competing Interactions, Spirals, and Phase Transitions with and without Long-Range Order

Abstract

An exactly solvable continuous-spin model with general exchange interactions is constructed and studied for cases of simple crystalline symmetry. For lattice dimensionality $D=2\mathrm{}$ the transition temperature $T_c$ goes to zero at the Lifshitz point. A particular case with $D=3\mathrm{}$ exhibits a phase transition with no long-range order.