Rocha Filho TM, Amato MA, Mello BA, Figueiredo A. Phase transitions in simplified models with long-range interactions.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011;
84:041121. [PMID:
22181101 DOI:
10.1103/physreve.84.041121]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2011] [Revised: 08/26/2011] [Indexed: 05/31/2023]
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.
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