Microcanonical Monte Carlo study of one dimensional self-gravitating lattice gas models

  • Joao Marcos Maciel
  • Marco Antônio Amato
  • Tarcisio Marciano da Rocha Filho
  • Annibal D. Figueiredo
Regular Article


In this study we present a microcanonical Monte Carlo investigation of one dimensional (1 − d) self-gravitating toy models. We study the effect of hard-core potentials and compare to the results obtained with softening parameters and also the effect of the topology on these systems. In order to study the effect of the topology in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as 1 /r model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the system that is redefined in terms of the packing fraction of the system. The latter plays a role similar to the softening parameter ϵ in the softened particles’ case. In the case of low packing fractions both models with hard-core particles show a behavior that keeps the intrinsic properties of the three dimensional gravitational systems such as negative heat capacity. For higher values of the packing fraction the ring model behaves as the potential for the standard cosine Hamiltonian Mean Field model while for the 1 /r model it is similar to the one-dimensional systems. In the present paper we intend to show that a further simplification level is possible by introducing the lattice-gas counterpart of such models, where a drastic simplification of the microscopic state is obtained by considering a local average of the exact N-body dynamics.


Statistical and Nonlinear Physics 


  1. 1.
    A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Campa, T. Dauxois, D. Fanelli, S. Ruffo, Physics of Long-Range Interacting Systems (Oxford University Press, Oxford, 2014)Google Scholar
  3. 3.
    F.B. Rizzato, R. Pakter, Y. Levin, Phys. Rev. E 80, 021109 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    T. Padmanabhan, Phys. Rep. 188, 285 (1990)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Venaille, T. Dauxois, S. Ruffo, arXiv:1503.07904 (2015)
  6. 6.
    A. Antoniazzi, Y. Elskens, D. Fanelli, S. Ruffo, Eur. Phys. J. B 50, 603 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    Lj. Milanović, H.A. Posch, W. Thirring, J. Stat. Phys. 124, 843 (2006)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    T.N. Teles, Y. Levin, R. Pakter, F.B. Rizzato, J. Stat. Mech. 2010, P05007 (2010)CrossRefGoogle Scholar
  9. 9.
    M. Antoni, S. Ruffo, Phys. Rev. E 85, 2361 (1995)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Sota, O. Igushi, M. Morikawa, T. Tatekawa, K. Maeda, Phys. Rev. E 64, 056133 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens, Dynamics and Thermodynamics of Systems with Long-Range Interactions (Springer, Berlin, 2002)Google Scholar
  12. 12.
    T. Tatekawa, F. Bouchet, T. Dauxois, S. Ruffo, Phys. Rev. E. 71, 056111 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    D. Lyndem-Bell, Mon. Not. Roy. Astron. Soc. 138, 495 (1968)ADSCrossRefGoogle Scholar
  14. 14.
    V.A. Antonov, Vest. Leningrad Gros. Univ. 7, 135 (1962) [English transl. in IAU Symposium 113, Dynamics of Globular Clusters, edited by J. Goodman, P. Hut (Dordrecht: Reidel, 1985), pp. 525-540]Google Scholar
  15. 15.
    D. Heggie, P. Hut, The Gravitational Million-Body Problem (Cambridge University Press, Cambridge, 2003)Google Scholar
  16. 16.
    F. Hohl, M.R. Feix, Astrophys. J. 147, 1164 (1967)ADSCrossRefGoogle Scholar
  17. 17.
    T. Tatekawa, F. Bouchet, T. Dauxois, S. Ruffo, Phys. Rev. E 52, 2361 (1995)Google Scholar
  18. 18.
    T.M. Rocha Filho, M.A. Amato, A. Figueiredo, Phys. Rev. E 71, 062103 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1997)Google Scholar
  20. 20.
    M.H. Kalos, P. Whitlock, in Monte Carlo Methods (Willey, New York, 1986), Vol. 1Google Scholar
  21. 21.
    D. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2009)Google Scholar
  22. 22.
    K. Binder, Rep. Prog. Phys. 60, 487 (1997)ADSCrossRefGoogle Scholar
  23. 23.
    J.M. Maciel, M.-C. Firpo, M.A. Amato, Physica A 424, 34 (2015)CrossRefGoogle Scholar
  24. 24.
    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)ADSCrossRefGoogle Scholar
  25. 25.
    M. Creutz, Phys. Rev. Lett. 50, 1411 (1983)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    J. Ray, Phys. Rev. A 44, 4061, (1991)ADSCrossRefGoogle Scholar
  27. 27.
    M. Kac, G. Uhlenbeck, P. Hemmer, J. Math. Phys. 4, 216 (1963)ADSCrossRefGoogle Scholar
  28. 28.
    W. Braun, K. Hepp, Commun. Math. Phys. 56, 125 (1977)CrossRefGoogle Scholar
  29. 29.
    P.-H. Chavanis, Physica A 361, 55 (2006)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    T.M. Rocha Filho, M.A. Amato, A.E. Santana, A. Figueiredo, J.R. Steiner, Phys. Rev. E 89, 032116 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    M.K.-H. Kieslling, J. Stat. Phys. 155, 1299 (2014)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    M. Champion, A. Alastuey, T. Dauxois, S. Ruffo, J. Phys. A 47, 225001 (2014)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    C. Nardini, L. Casetti, Phys. Rev. E 80, 060109 (2009)CrossRefGoogle Scholar
  34. 34.
    T.M. Rocha Filho, M.A. Amato, B.A. Mello, A. Figueiredo, Phys. Rev. E 84, 041121 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Joao Marcos Maciel
    • 1
  • Marco Antônio Amato
    • 1
    • 2
  • Tarcisio Marciano da Rocha Filho
    • 1
    • 2
  • Annibal D. Figueiredo
    • 1
    • 2
  1. 1.Instituto de Física, Universidade de BrasíliaBrasíliaBrazil
  2. 2.International Center for Condensed Matter Physics, Universidade de BrasíliaBrasíliaBrazil

Personalised recommendations