The Effect of Lattice Vibration on the Phase Transition of the Ising Model

Abstract

The effect of lattice vibration on the second-order phase transition for the Ising model is investigated. The total Hamiltonian of the system is separated into the phonon part and the spin part, if the displacement of the atoms from their equilibrium position is assumed to be small. The spin part of the free energy is then calculated (i) in the molecular-field approximation for the square and the simple cubic lattices, and (ii) by the method due to Kadanoff, a modification of the Onsager's exact solution, for the square lattice. The results show that (i) the phase transition remains to be of the second order, (ii) the critical temperature increases, and (iii) the magnetic part of the heat capacity decreases, both for ferro- and antiferromagnetic Ising models.