Phase diagrams and higher-order critical points

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Abstract
A classification scheme is presented for the different entities one might expect to find in phase diagrams of fluid mixtures (or other systems where the phases do not break the symmetry of the Hamiltonian) when critical phenomena are present. These include critical points and critical end points of various sorts, higher-order critical points, and entities coexisting in distinct phases. The classification scheme employs the topological properties of the phase diagram, in a space of field variables (temperature, chemical potentials), in the immediate vicinity of the point in question. A graphical method is given for representing some of the topological information in the phase diagram. The entities obtained using a Landau model with one order parameter are discussed and some preliminary results are presented for the case of two order parameters. A phase diagram for a possible fluid analog of the two-dimensional three-state Potts model is described.