On the solutions of the $Z_n$-Belavin model with arbitrary number of   sites
  The periodic $Z_n$-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. 
Kun Hao, Junpeng Cao, Guang-Liang Li, Wen-Li Yang, Kangjie Shi, Yupeng   Wang
math-ph cond-mat.stat-mech hep-th math.MP