Statistical mechanics of an elastic Ising chain with exchange striction

The transfer matrix method is used in a rigorous study of the statistical mechanics of an elastic chain of atoms having spin moment $1/2$. The chain is situated in a diamagnetic crystal whose influence on the chain is represented in the form of the potential $\varphi^2$. The spins are coupled by a short-range exchange interaction whose magnitude is a function of the distance between the spins. The single-ion coupling of the spins with the displacements of the atoms of the chain is also taken into account.