Phase Transitions in Systems with 1/rα Attractive Interactions

  • Eddie G. D. Cohen
  • Iaroslav Ispolatov
Part of the Lecture Notes in Physics book series (LNP, volume 602)


We study the gravitational collapse — like phase transitions in the microcanonical ensemble for a class of systems of N particles with nonintegrable attractive pair potentials 1/r α, with 0 < α < 3 in three dimensions. Introducing a continuum description and a mean field approximation in the limit N to infinity, an integral equation for the density profile of the particles is obtained, which is solved numerically. For all 0 < α < 3 and sufficiently small short range cutoffs r 0, there appears to be cutoff-independent critical energy, below which the system jumps discontinuously from a normal uniform to a collapsed core — halo state. This gravitational-like transition will become a normal first order transition when the cutoff range r 0 becomes larger than some critical value r 0c which is an increasing function of α.


Phase Transition Order Transition Order Phase Transition Attractive Interaction Collapse State 
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  1. 1.
    I. Ispolatov, E. G. D. Cohen: Phys. Rev. Lett. 87, 210601 (2000); Phys. Rev. E 64, 056103 (2000)CrossRefGoogle Scholar
  2. 2.
    See, e.g., T. Padmanabhan, Phys. Rep. 188, 285 (1990)CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    J. Barré, D. Mukamel, S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001), I. Ispolatov, E. G. D. Cohen, Physica A 295, 475 (2001)CrossRefADSGoogle Scholar
  4. 4.
    D. Gross, Microcanonical Thermodynamics, World Scientific Lecture Notes in Physics, Vol.66, World Scientific Singapore (2001)Google Scholar
  5. 5.
    P.H. Chavanis, I. Ispolatov: Phys. Rev. E 66, 036109 (2002)CrossRefADSGoogle Scholar
  6. 6.
    L. Casetti, E. G. D. Cohen, in preparationGoogle Scholar
  7. 7.
    H.J. de Vega, N. Sanchéz, Nucl. Phys. B 625, 409 (2002)zbMATHCrossRefADSGoogle Scholar
  8. 8.
    V.P. Youngkins, B. N. Miller, Phys. Rev. E. 62, 4583 (2000)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Eddie G. D. Cohen
    • 1
  • Iaroslav Ispolatov
    • 2
  1. 1.Center for Studies in Physics and BiologyThe Rockefeller UniversityNew YorkUSA
  2. 2.Departamento de FísicaUniversidad de Santiago de ChileSantiagoChile

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