Exact thermodynamics of a generalized compressible Ising model in one dimension

We propose a generalized compressible Ising model and solve it exactly, using the renormalization-group method. We obtain exact expressions for free energy and spin-spin correlation functions for periodic and free boundary condition in a finite chain or in the thermodynamic limit. Through this method, we develop functional recursion relations. The corresponding fixed points are investigated with the correlation length. Our method is applicable to higher-order correlation functions.