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

TL;DR

This paper extends the classical scaling laws of second order phase transitions to higher order transitions, establishing relations between critical exponents and discussing implications for superconducting materials and thin films.

Contribution

It generalizes scaling laws to arbitrary higher order phase transitions, linking exponents of different observables regardless of fluctuation effects.

Findings

Derived relations between critical exponents for higher order transitions.

Applicable to superconducting transitions in specific materials.

Discussed phase transition behavior in thin films.

Abstract

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.