Another Checkpoint for Second Order Transitions Equivalent to the Checkpoint of Positive Definiteness and Incompatible Inequalities

Abstract

In the previous paper [JPSJ 47 (1979) 1773], the checkpoint of positive definiteness and incompatible inequalities was offered and applied to several transitions. In the present paper another checkpoint is offered and applied to the same transitions. This checkpoint does not seek the eigenvalues of the matrix (∂²Ψ⁄∂Q_i∂Q_j)_s of the ferroic in question (where Q₁, Q₂, ···denote the transition parameters; Ψ the thermodynamic potential function; s “spontaneous”). Instead it compares the second or higher order curvature of the Ψ_s of the ferroic in question with those of all other maximal-rank ferroics. For all the above-mentioned transitions the present checkpoint is found to give the same incompatible or compatible inequalities and hence the same conclusions on orders as the previous checkpoint gave.