The critical properties of ferrodistortive spin-phonon systems

The form of the Landau-Ginsburg effective Hamiltonian is derived for a spin-phonon coupled system. For T D not=0 it is found that both the quadratic and quartic terms reduce to those for an Ising model with a non-analytic form for J(q). A crossover calculation (to order epsilon ) is performed to evaluate the way in which the effective susceptibility exponent gamma will vary with t as the non-analytic terms drive the system away from the Ising to the gaussian fixed point.