On a New Class of Phase Transitions

R. Hilfer

in: Random Magnetism and High-Temperature Superconductivity
edited by: W.P. Beyermann and N.L. Huang-Liu and D.E. MacLaughlin
World Scientific Publ. Co., Singapore, 85 (1994)

submitted on
Friday, March 19, 1993

A recently introduced classification theory for phase transitions characterizes each phase transition by its generalized noninteger order and a slowly varying function. Thermodynamically this characterization arises from generalizing the classification scheme of Ehrenfest. The same characterization emerges in statistical mechanics from generalizing the finite size scaling limit. The classification theory predicts an unusual class of phase transitions characterized by fractional orders less than unity. Examples are found in unstable models of statistical mechanics. Finally it is shown how the statistical classification theory gives rise to a classification of macroscopic dynamical behaviour based on a generalization of the stationarity concept.

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