A Comment on the beta-expansion of s=1/2 and s=1 Ising Models
  The purpose of the present work is to apply the method recently developed in reference [chain_m] to the spin-1 Ising chain, showing how to obtain analytical $\beta$-expansions of thermodynamical functions through this formalism. In this method, we do not solve any transfer matrix-like equations. A comparison between the $\beta$-expansions of the specific heat and the magnetic susceptibility for the $s=1/2$ and $s=1$ one-dimensional Ising models is presented. We show that those expansions have poorer convergence when the auxiliary function of the model has singularities. 
Winder A. Moura-Melo, Onofre Rojas, E.V. Correa Silva, S.M. de Souza   and M.T. Thomaz