A deduction of the multicriticality conditions of mixtures from the Gibbs tangent plane criterion

Here, we follow a classification proposed by Griffiths and Widom [1], where the order of a multicritical point in a mixture is equal to the number of phases which simultaneously become identical, considering m phases and assuming that m − 1 of these phases become identical to a given test phase. Thus, employing Rolleʹs theorem and basic properties of the so-called tangent-plane distance function, we develop a deduction of the multicriticality conditions of mixture from Gibbs tangent plane criterion, which relies on the principle of mathematical induction, being appropriate for any m ≥ 2.