Abstract
For pt. II see abstr. A62238 of 1971. The effective spin hamiltonian containing a four-spin term which arises from allowing harmonic phonons to be included in the Ising model was solved to molecular field approximation (MFA) in an earlier paper by two of the authors. A brief review is given of the MFA results with two methods of deriving the result both simpler than that of the first publication. The need for employing the ensemble average of the nearest neighbour correlation function is pointed out and it is shown that in this model the elastic strain in the lattice is proportional to this correlation function. The problem is then studied at an approximation equivalent to the quasichemical or Bethe-Peierls results for the pure Ising model and both the long range order and this correlation function are employed explicitly. As in the MFA, the nature of the phase transition changes from second order to first order as the strength of the spin-phonon coupling is increased. High temperature contributions to thermal expansion are calculated.
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