Ferrimagnetic-helimagnetic transition in an XY magnet with infinitely many phases

The authors present an anisotropic frustrated classical spin model, in which the coexistence of continuous and discrete degrees of freedom can be explicitly considered. They investigate an array of planar (XY) spins with usual bilinear exchange, on decorated lattices both in two and three dimensions, whose zero-temperature state is infinitely degenerate. The set of ground states includes a uniform ferrimagnetic arrangement, a uniform helimagnet, and any arbitrary admixture of these in the form of coexisting striped domains. Each ground state in the degeneracy manifold can be exactly mapped to a specified configuration of an anisotropic Ising model on the dual lattice. Ising spins represent the discrete chirality degrees of freedom. Low-temperature continuous excitations (spin waves) couple these Ising spins, selecting the configuration corresponding to the ferrimagnetic state (order by thermal disorder). Adding a competing next-nearest-neighbour interaction allows one to tune a transition to the helimagnet; at low temperature the transition occurs through an infinite sequence of steps, consisting of first-order phase transitions to successive ferrimagnetic phases, each made of helimagnetically ordered stripes of constant width. The width increases from phase to phase, and chirality alternates from stripe to stripe. A discussion of the relationship between decorated continuous spin models and multi-spin interaction is given.