Magnetic field influence on the spin-Peierls instability in the quasi-one-dimensional magnetostrictive $\mathrm{XY}$ model: Thermodynamical properties

We study in detail, within the adiabatic approximation for the structural degrees of freedom and on exact grounds for the magnetic ones, the $d=1\mathrm{}$ magnetostrictive spin-½ $\mathrm{XY}$ model in the presence of an external magnetic field along the $z$ axis. We calculate the specific heat, magnetization, isothermal susceptibility, and the structural order parameter and spectrum (including the sound velocity). The system presents, in temperature-field space, three structurally different phases: the uniform ($U$), the dimerized ($D$), and the modulated ($M$) phases (the latter can be either commensurate or incommensurate with the other two). The critical frontiers $U-D$ and $U-M$ are of the second-order type while the $D-M$ one is of the first-order type; all three join at a Lifshitz point. The $U-M$ frontier presents a new type of multicritical point on which the frozen structural wave vector vanishes. The phase diagram is quite anomalous for high values of the elastic constant. Several other effects are predicted. The present theory is expected to be applicable to substances like TTF-BDT [tetrathiafulvalinium bis-cis-(1,2-perfluoromethylethylene-1,2-diselenolato)-metal], ${\mathbf{MEM}\left(\mathbf{TCNQ}\right)\mathrm{}}_2$ (N-methyl-N-ethyl-morpholinium ditetracyanoquinodimethanide), and eventually the alkali-metal tetracyanoquinodimethanides (TCNQ).