Critical behavior of an Ising spin system coupled to acoustic and optic lattice modes

Abstract

An isotropic compressible Ising model is considered where, besides the coupling of the spins to the acoustic modes of the lattice, coupling to the optic modes is also assumed to exist. It is shown that, under constant volume and pinned boundary conditions, for T very near T,, the critical behaviour is not changed, as compared to the situation where only coupling to acoustic phonons is considered; the system shows Fisher-renormalised critical exponents. However, the size of the region where this behaviour is observed depends on the coupling to optic phonons, as does the phonon correlation function. The size of the first- order transition to occur under free-boundary conditions is shown to be enhanced when coupling to optic modes is taken into consideration.