The Topological Nonconnectivity Threshold and magnetic phase transitions in classical anisotropic long-range interacting spin systems

  • R. Trasarti-Battistoni
  • F. Borgonovi
  • G. L. Celardo
Hamiltonian Systems


We review, with emphasis on the dynamical point of view, the classical characteristics of the Topological Nonconnectivity Threshold (TNT), recently introduced in F. Borgonovi, G.L. Celardo, M. Maianti and E. Pedersoli, J. Stat. Phys. 116, 1435 (2004). This shows interesting connections among Topology, Dynamics, and Thermo-Statistics of ferro/paramagnetic phase transition in classical spin systems, due to the combined effect of anisotropy and long-range interactions.


05.45.-a Nonlinear dynamics and nonlinear dynamical systems 05.45.Pq Numerical simulations of chaotic systems 75.10.Hk Classical spin models  


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  1. E.M. Chudnovsky, J. Tejada, Macroscopic Quantum Tunneling of the Magnetic Moment (Cambridge University Press, 1998) Google Scholar
  2. D. Lynden-Bell, R. Wood, Mon. Not. R. Astr. Soc. 136, 101 (1967); W. Thirring, Z. Phys. 235, 339 (1970); D. Lynden-Bell, R. M. Lynden-Bell, Mon. Not. R. Astr. Soc. 181, 405 (1977); D. Lynden-Bell, e-print arXiv:cond-mat/9812172 ADSGoogle Scholar
  3. J. Barré, D. Mukamel, S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001) CrossRefADSGoogle Scholar
  4. J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, Phys. Rev. Lett. 89, 110601 (2002) CrossRefADSGoogle Scholar
  5. G.L. Celardo, Ph.D. dissertation, University of Milano, Italy (2004) Google Scholar
  6. F. Borgonovi, G.L. Celardo, M. Maianti, E. Pedersoli, J. Stat. Phys. 116, 1435 (2004) CrossRefMathSciNetGoogle Scholar
  7. F. Borgonovi, G.L. Celardo, G.P. Berman, e-print arXiv:cond-mat/0506233, accepted for publication in PRB, F. Borgonovi, G.L. Celardo, R. Trasarti-Battistoni, e-print arXiv:cond-mat/0510079 Google Scholar
  8. R.G. Palmer, Adv. in Phys. 31, 669 (1982) CrossRefADSGoogle Scholar
  9. A.I. Khinchin Mathematical Foundations of Statistical Mechanics (Dover Publications, New York, 1949) Google Scholar
  10. L. Caiani et al., Phys. Rev. Lett. 79, 4361 (1997); L. Casetti et al., Phys. Rep. 337, 237 (2000); L. Casetti et al., J. Stat. Phys. 111, 1091 (2003); R. Franzosi, M. Pettini, Phys. Rev. Lett. 92, 060601 (2004); R. Franzosi et al., arXiv:cond-mat/05005057; R. Franzosi et al., arXiv:cond-mat/05005058 CrossRefGoogle Scholar
  11. M. Kastner, Phys. Rev. Lett. 93, 150601 (2004); I. Hahn, M. Kastner, e-print arXiv:cond-mat/0506649; I. Hahn, e-ptint arXiv:cond-mat/0509136; M. Kastner, e-ptint arXiv:cond-mat/0509206, L. Angelani, G. Ruocco, F. Zamponi, Phys. Rev. E 72, 016122 (2005) CrossRefADSGoogle Scholar
  12. D.H.E. Gross, Phys. Rep. 279, 119 (1997); D.H.E. Gross Microcanonical Thermodynamics: Phase Transitions in Small Systems, Lecture Notes in Physics 66 (World Scientific, Singapore, 2001) CrossRefADSGoogle Scholar
  13. G.L. Celardo, J. Barré, F. Borgonovi, S. Ruffo, e-print arXiv:cond-mat/04010119 Google Scholar
  14. Dynamics and Thermodynamics of Systems with Long Range Interactions, edited by T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens, Lectures Notes in Physics 602, Springer (2002) Google Scholar
  15. F. Borgonovi, G.L. Celardo, A. Musesti, R. Trasarti-Battistoni, P. Vachal, e-print arXiv:cond-mat/0505209 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • R. Trasarti-Battistoni
    • 1
  • F. Borgonovi
    • 1
    • 2
  • G. L. Celardo
    • 1
  1. 1.Dipartimento di Matematica e FisicaUniversità CattolicaBresciaItaly
  2. 2.I.N.F.N.Sezione di PaviaItaly

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