Inversion Method Based on the Legendre Transformation Applied to Discontinuous Phase Transitions

抄録

We investigated a model of a nematic–isotropic (NI) transition, whose mean-field approximation coincides with Maier–Saupe (MS) theory, by Fukuda’s inversion method (IM), which is based on the Legendre transformation and is similar to a method of symmetry-breaking potential. The first-order approximation of this nonperturbative method neglects fluctuations and reproduces the MS theory, predicting a weakly discontinuous phase transition at the MS transition temperature T_MS. The second-order IM approximation allows us to include fluctuations, which suppress the phase transition.