Villain transformation for ferrimagnetic spin chain with dimerization

The dimerized ferrimagnetic spin chain has been approached both in the presence and absence of the external magnetic field by using the Villain transformation. Two branches of the low-lying energy modes have been presented and the upper branch of the mode demonstrates the exotic omega-shape when the dimerization parameter is greater than 0.6. We also find that the competition between magnetic field and the dimerization parameter also contribute the omega-shape in lower branch mode. Thermodynamic quantities like free energy, specific heat, magnetization, and susceptibility in finite temperature and magnetic field with different dimerization parameters have also been presented.