Spin-Peierls instability in the quasi d=1 magnetostrictive XY model

Within a framework where the magnetic (structural) degrees of freedom are exactly (adiabatically) taken into account, the spin-Peierls instability occuring in the magnetically one-dimensional and structurally three-dimensional magnetostrictive spin-1/2 XY model is discussed. Emphasis is given to the influence of an external magnetic field (along the Z-axis) on the thermodynamical (phase diagram, structural order parameter, specific heat, magnetization, susceptibility) and dynamical (acoustic and optic phonons spectrum) quantities. It is recovered and extended several already known results; furthermore a certain amount of facts is established and possible new effects are exhibited. In the T-H phase diagram, a structural Lifshitz point (LP) exists where the uniform (U), pure dimerized (D) and modulated (M) phases converge (the relative arrivals, on the LP, of the three critical and two metastability lines are determined); another special point is detected on the U-M line at large magnetic fields; the slope of the D-M first-order frontier is discussed; for high elastic constants, fixed temperatures and increasing magnetic field, the unusual sequence (non uniform) - uniform - (non uniform) - uniform is possible. The thermal dependence of the sound velocity presents a gap. The present theory is hopefully applicable (at least qualitatively) to substances like TTF-BDT, MEM(TCNQ)2 and eventually alkali-TCNQ. (Author)