Nonlinear Coupling among Critical Fluctuations: A Possible Source of Weak Divergences at a Critical Point

Abstract

It is shown that a nonlinear coupling among critical fluctuations produces weak divergences in certain thermodynamic derivatives in agreement with the scaling law predictions. Moreover, restricting our analysis to quadratic terms in the order parameter fluctuations, an explicit expression is provided for the amplitude of the singularities. Weak divergences in binary mixtures are discussed in detail, including several exceptional cases, such as critical azeotropy. No divergence is predicted in general for the heat capacity at constant volume and concentration.