- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Coevolution of Glauber-like Ising dynamics and topology

Salvatore Mandrà1,2, Santo Fortunato3, and Claudio Castellano4

  • 1Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
  • 2INFN, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
  • 3Complex Networks Lagrange Laboratory, ISI Foundation, Torino, Italy
  • 4SMC, INFM-CNR and Dipartimento di Fisica, “Sapienza” Università di Roma, P.le Aldo Moro 2, I-00185 Roma, Italy

PDF

Phys. Rev. E 80, 056105 – Published 13 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.056105

Abstract

We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.

View figure in article

Article Text

References (23)

  1. C. Castellano, S. Fortunato, and V. Loreto, Rev. Mod. Phys. 81, 591 (2009).
  2. J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman, The Theory of Critical Phenomena (Oxford University Press, Oxford, England, 1992).
  3. M. E. J. Newman, SIAM Rev. 45, 167 (2003).
  4. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 424, 175 (2006).
  5. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
  6. M. G. Zimmermann, V. M. Eguíluz, and M. San Miguel, Phys. Rev. E 69, 065102(R) (2004).
  7. G. C. M. A. Ehrhardt, M. Marsili, and F. Vega-Redondo, Phys. Rev. E 74, 036106 (2006).
  8. P. Holme and M. E. J. Newman, Phys. Rev. E 74, 056108 (2006).
  9. D. H. Zanette and S. Gil, Physica D 224, 156 (2006).
  10. A. Grabowski and R. A. Kosiński, Phys. Rev. E 73, 016135 (2006).
  11. D. Centola, J. C. González-Avella, V. M. Eguíluz, and M. San Miguel, J. Conflict Resolut. 51, 905 (2007).
  12. F. Vazquez, J. C. Gonzalez-Avella, V. M. Eguíluz, and M. San Miguel, Phys. Rev. E 76, 046120 (2007).
  13. F. Vazquez, V. M. Eguíluz, and M. San Miguel, Phys. Rev. Lett. 100, 108702 (2008).
  14. C. Nardini, B. Kozma, and A. Barrat, Phys. Rev. Lett. 100, 158701 (2008).
  15. B. Kozma and A. Barrat, Phys. Rev. E 77, 016102 (2008).
  16. I. J. Benczik, S. Z. Benczik, B. Schmittman, and R. K. P. Zia, EPL 82, 48006 (2008).
  17. P. Klimek, R. Lambiotte, and S. Thurner, EPL 82, 28008 (2008).
  18. R. J. Glauber, J. Math. Phys. 4, 294 (1963).
  19. M. Granovetter, Am. J. Sociol. 83, 1420 (1978).
  20. P. Erdös and A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959).
  21. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
  22. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994).
  23. If no such node exists no action is taken.

Outline

Information

Phys. Rev. E 80, 056105– Published 13 November, 2009
  • Received 13 June 2009

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation