Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws

Details Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws

2002-04-30

arxiv.org/abs/cond-mat/0205002v1

Philosophical Magazine B82, 1201-1209 (2002)

Physics

Condensed Matter

Superconductivity

10 pages, no figures

Scientific paper

10.1080/13642810210127011

The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the superconducting transition in Ba$_{0.6}$K$_{0.4}$BiO$_3$ and in Bi$_2$Sr$_2$CaCu$_2$O$_8$, there are singularities in higher order derivatives of the free energy. A relation between exponents of different observables has been found, regardless of whether the exponents are classical (mean-field theory, no fluctuations, integer order of a transition) or not (fluctuation effects included). We also comment on the phase transition in a thin film.

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