On the solutions of the Zn-Belavin model with arbitrary number of sites

The periodic Zn-Belavin model on a lattice with an arbitrary number of sites N is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified inhomogeneous T−Q relation. In the special case of N=nl with l being also a positive integer, the resulting T−Q relation recovers the homogeneous one previously obtained via algebraic Bethe Ansatz.