A Spin Glass Model with Vibrations of Crystal Lattices

With the help of the replica method and imaginary-time functional-integrate technique, the spin glass model with the vibrations of crystal lattices is investigated. In the limit of the replica symmetry and the imaginary-time static approximation, the magnetic and thermodynamic quantities have been obtained. By the numerical calculations, we found that the magnetization of the system has the typical spin-glass behaviour. A peak is found in the susceptibility--temperature curve and is shifted to lower temperature with increasing applied field. Due to the lattice contribution, the specific heat increases strongly at high temperature. Due to the magnetic contribution, the anomaly in the specific heat--temperature curve forms a λ-type peak, which agrees with the observation of Rojo et al. Phys. Rev. B 66 (2002) 094406.