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Some statistical equilibrium mechanics and stability properties of a class of two-dimensional Hamiltonian mean-field models

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  • Maciel, J.M.
  • Firpo, M.-C.
  • Amato, M.A.

Abstract

A two-dimensional class of mean-field models that may serve as a minimal model to study the properties of long-range systems in two space dimensions is considered. The statistical equilibrium mechanics is derived in the microcanonical ensemble using Monte Carlo simulations for different combinations of the coupling constants in the potential leading to fully repulsive, fully attractive and mixed attractive–repulsive potential along the Cartesian axis and diagonals. Then, having in mind potential realizations of long-range systems using cold atoms, the linear theory of this two-dimensional mean-field Hamiltonian models is derived in the low temperature limit.

Suggested Citation

  • Maciel, J.M. & Firpo, M.-C. & Amato, M.A., 2015. "Some statistical equilibrium mechanics and stability properties of a class of two-dimensional Hamiltonian mean-field models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 34-43.
    • Handle: RePEc:eee:phsmap:v:424:y:2015:i:c:p:34-43
    DOI: 10.1016/j.physa.2014.12.030
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    References listed on IDEAS

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    1. Pluchino, Alessandro & Andronico, Giuseppe & Rapisarda, Andrea, 2005. "A Monte Carlo investigation of the Hamiltonian mean field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 143-154.
    2. Chavanis, Pierre-Henri, 2006. "Quasi-stationary states and incomplete violent relaxation in systems with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 102-107.
    3. Pluchino, Alessandro & Rapisarda, Andrea & Tsallis, Constantino, 2008. "A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3121-3128.
    4. Yamaguchi, Yoshiyuki Y. & Barré, Julien & Bouchet, Freddy & Dauxois, Thierry & Ruffo, Stefano, 2004. "Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 36-66.
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    Cited by:

    1. Chrisment, Antoine M. & Firpo, Marie-Christine, 2016. "Entropy–complexity analysis in some globally-coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 162-173.

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