Villain transformation theory of the anisotropy ferrimagnetic spin chain

By using the Villain transformation, the Heisenberg ferrimagnetic spin chain with anisotropy D˜ as well as an external field is explored. We obtain two branches of the low-lying excitation spectrum with the presence of magnetic field. The thermodynamic quantities, like free energy, specific heat and magnetization at finite temperature, are calculated. And the effects of the anisotropy parameter D˜ on these thermodynamic quantities are explicitly discussed. The results show that a phase transition may occur at the critical value of anisotropy D˜=0.3.