title: Phase transitions in simplified models with long-range interactions.
abstract: We study the origin of phase transitions in several simplified models with long-range interactions. For the self-gravitating ring model, we are unable to observe a possible phase transition predicted by Nardini and Casetti [Phys. Rev. E 80, 060103R (2009).] from an energy landscape analysis. Instead we observe a sharp, although without any nonanalyticity, change from a core-halo to a core-only configuration in the spatial distribution functions for low energies. By introducing a different class of solvable simplified models without any critical points in the potential energy we show that a behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features for the simplified models and show that the first-order phase transition comes from the maximization of the entropy of the system as a function of energy and an order parameter, as previously discussed by Hahn and Kastner [Phys. Rev. E 72, 056134 (2005); Eur. Phys. J. B 50, 311 (2006)], which seems to be the main mechanism causing phase transitions in long-range interacting systems.
authors.affiliation: Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, Caixa Postal 04455, 70919-970 Brasília, Distritio Federal, Brazil.
authors.forename: T M
authors.initials: TM
authors.lastname: Rocha Filho
authors.forename: M A
authors.initials: MA
authors.lastname: Amato
authors.forename: B A
authors.initials: BA
authors.lastname: Mello
authors.forename: A
authors.initials: A
authors.lastname: Figueiredo