On the degree of ultrametricity

R. Rammal , Jean-Christian Anglès d'Auriac , Benoît Douçot

Using the notion of the subdominant ultrametric, the degree of ultrametricity D of a given metric space (e.g. phase space) is introduced. A simple and efficient method for the calculation of D is outlined. D is shown to provide a simple quantitative measure of the deviation from exact ultrametricity. Explicit examples are used to illustrate this notion which is argued to be of some interest in statistical-mechanical models and combinatorial optimization problems.

Mots clés: statistical mechanics; ultrametricity; subdominant ultrametric; metric space; phase space; statistical mechanical models; combinatorial optimization

Domaines: Articles anciens

R. Rammal, Jean-Christian Anglès d'Auriac, Benoît Douçot. On the degree of ultrametricity. Journal de Physique Lettres, 1985, 46 (20), pp.945-952. ⟨10.1051/jphyslet:019850046020094500⟩. ⟨jpa-00232922⟩