Dynamic Susceptibility of Classical Anharmonic Oscillator

Abstract

As a unified oscillator model for order-disorder and displacive ferroelectrics, we consider a system of interacting classical oscillators moving in the anharmonic potential V(x) = Ax4 + Bx2, where A is positive and B may be either positive or negative. The interaction of the oscillators is taken to be bilinear in their displacements and it is treated in the Weiss molecular-field approximation. For this model, it is shown that the exact expression can be obtained for the dynamic susceptibility above the Curie temperature. The theory is exact except for its being classical and use of the Weiss approximation; anharmonicity of the potential is perfectly taken into account. Detailed analysis is made for this system and temperature dependence of the dynamic response (including the occurrence of “soft” mode) is described on the basis of the results of numerical calculations for both B > 0 and B ≪ 0 cases.