Thermodynamics of an alternate σ=1 and Ising chain mapped onto an effective BEG model

A linear chain of alternate Ising spins σ=1 and , with bi-linear, bi-quadratic, single-ion and Zeeman interactions is studied. It is shown that this system can be mapped onto an effective BEG model, by the use of an extended decoration transformation. Exact results are obtained for the ground-state phase diagram and thermodynamical responses such as specific heat and magnetic susceptibility are shown.