Spin anisotropy effects on the dimerization of the magnetostrictive quasi-one-dimensional XY model

The one-dimensional first-neighbour spin - $\text{1}\text{2}$ magnetostrictive XY model (with crystalline degrees of freedom assumed three- dimensional) with $\text{different}$ X and Y spin coupling constants presents a quite rich spin-Peierls dimerization phase diagram. In the (low anisotropy) - (low temperature) region we recover previous results (in particular the possibility for a first-order phase transition in the absence of external magnetic field); in the other three regions of the temperature-anisotropy space interesting branches of the phase diagram (including the tricritical line) are exhibited (for the first time as far as we know).