Villain Transformation for Ferrimagnetic Spin Chain

By using the Villain transformation, the Heisenberg ferrimagnetic spin chain is calculated. Two branches of the low-lying excitation in both the absence and presence of magnetic field are obtained. The thermodynamic quantities (such as free energy, magnetization, specific heat and static magnetic susceptibility) are also evaluated at finite temperature. This is the first time to calculate the Ferrimagnetic spin chain by using Villain's method, and we find that the results at a low temperature are quite similar to the previous calculation. The results of free energy and magnetization in zero temperature suggest that the Villain transformation has a good efficiency.