Thermodynamics of a higher-order phase transition: Scaling exponents and scaling laws

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 suggested for the superconducting transition in Ba_0.6K_0.4BiO₃ and in Bi₂Sr₂CaCu₂O₈, 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.