Magnetic phase transitions on elastic isotropic lattices

The elimination of the elastic degrees of freedom of a harmonic isotropic lattice transforms the magnetoelastic coupling into an effective magnetic interaction which consists of a short-range interaction recently discussed by Aharony and a long-range interaction due to the free surface of the systems. Within the renormalization group approach to critical phenomena it is shown that the critical behaviour of the system is described appropriately by the magnetothermomechanics provided that the additional short-range interaction does not change the critical behaviour.