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Center for Nonlinear Studies |
Following the discovery of the "lambda"-like anomaly in the specific heat of Helium at the superfluid transition, Ehrenfest postulated the existence of higher order phase transitions. These transitions are described by a remarkable class of free energies. As a function of the order parameter phi(r), the non-quadratic term in the free energy appears with an exponent 2p/(p-1). These free energies are interestingly related to the action for Tachyon condensation in field theory, as well as for the Fisher equation (and the generalized Fisher equation), a model for interaction between diffusion and reaction in physical as well biological systems. A curious limiting case of an infinite order phase transition is described by a free energy F = f^2 ln f where f is the order parameter.