title: Use of the cage formation probability for obtaining approximate phase diagrams.
abstract: In this work, we introduce the idea of cage formation probability, defined by considering the angular space needed by a particle in order to leave a cage given an average distance to its neighbors. Considering extreme fluctuations, two phases appear as a function of the number of neighbors and their distances to a central one: Solid and fluid. This allows us to construct an approximated phase diagram based on a geometrical approach. As an example, we apply this probability concept to hard disks in two dimensions and hard spheres in three dimensions. The results are compared with numerical simulations using a Monte Carlo method.
authors.affiliation: Departamento de Física-Química, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apartado Postal 20-364, 01000 Distrito Federal, Mexico.
authors.forename: Atahualpa S
authors.initials: AS
authors.lastname: Kraemer
authors.forename: Gerardo G
authors.initials: GG
authors.lastname: Naumis