Degeneracy and the Order of the Phase Transformation in the Molecular-Field Approximation

Abstract

An elementary analysis is given of the conditions for phase transformations of the first and second orders, in the molecular-field approximation. The analysis may be relevant to some ferroelectric, Jahn-Teller, order-disorder, and singlet-triplet transitions. On the assumptions of our two-level model, no transition can occur if the degeneracy of the ground state is higher than that of the excited state. A second-order transition can occur only if a special relation is satisfied between the coefficients of the terms in the energy which are linear and quadratic in the order parameter. A necessary condition for a first-order transition is that the degeneracy of the excited state be higher than that of the ground state. Under certain conditions the excitation density at the transition temperature is predicted to exceed that at infinite temperature: We may call this a supertransition.