First order phase transition in an anharmonic ising lattice

Criteria are derived for the existence of a first order phase transition in a compressible anharmonic Ising lattice. The analysis is based on a variational calculation and on the assumption that a compressible harmonic Ising lattice does not show a first order transition. A first order transition can occure only if the lattice and magnetic Grüneisen constants have the same sign and if the pressure is below some critical value. At this pressure the transition changes from first to second order. The results are applied to ammonium cloride exhibiting an order disorder transition of this type.