Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. We show that ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph - points are plotted as coordinates and joined by either a ...

In this paper we study the adelic zeta function associated with the prehomogeneous vector space of binary cubic forms, defined over a function field. We establish its rationality, find its poles and ...