Spin-Peierls transition of the anisotropic XY model in a magnetic field: Thermodynamic properties

The spin-Peierls phase transition for a quasi-one-dimensional XY chain is studied as a function of the degree of anisotropy of the exchange interaction (γ) and of the magnetic field (H). It is found that both anisotropy and magnetic field decrease the critical temperature. When γ and H progressively increase, the phase transition is first of second order, passes to first order, and finally the ordered phase completely disappears. The corresponding magnetization, magnetic susceptibility, and specific heat are given. In particular, a peak and a discontinuity in the magnetic susceptibility for finite magnetic field are found at the critical temperature, this discontinuity being maximum at the tricritical point separating the first- and second-order lines. For a second-order transition the magnetization behaves continuously through the critical point where a discontinuity is present only in the first derivative with respect to temperature. For the first-order case a discontinuity is present.