- 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

Critical behavior of a dynamic analog to the q=3 Potts model

Elena Salazar-Neumann, María Cristina Vargas*, and Gabriel Pérez

  • Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Unidad Mérida Apartado Postal 73 “Cordemex,” 97310 Mérida, Yucatán, Mexico

  • *Electronic address: cristina@mda.cinvestav.mx
PDF

Phys. Rev. E 71, 036228 – Published 31 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036228

Abstract

We construct a dynamical analog to the q=3 Potts model, using linear chaotic maps and a diffusive coupling. We find well-defined order-disorder phase transitions (PTs) in the system, and obtain the phase diagrams for both simultaneous and sequential updating of the model. For simultaneous updating we find continuous PTs whose critical exponents are consistent with those of the equilibrium Potts model. Under sequential updating, the phase diagram shows a tricritical point, and the PTs become first order for large coupling and chaoticity of the local maps. A preliminary estimation finds critical exponents in the region of continuous PTs that are not consistent with those of the equilibrium model.

View figure in article

Article Text

References (29)

  1. K. Kaneko, Prog. Theor. Phys. 72, 480 (1984).
  2. K. Kaneko, Physica D 37, 60 (1989).
  3. K. Kaneko, Physica D 41, 137 (1990).
  4. G. Pérez, S. Sinha, and H. Cedeira, Physica D 63, 341 (1993).
  5. H. Chaté and P. Manneville, Chaos 2, 307 (1992).
  6. H. Chaté and P. Manneville, Europhys. Lett. 17, 291 (1992).
  7. H. Chaté and P. Manneville, Prog. Theor. Phys. 87, 1 (1992).
  8. Theory and Applications of Coupled Map Lattices, edited by K. Kaneko (Wiley, New York, 1993).
  9. J. Miller and D. Huse, Phys. Rev. E 48, 2528 (1993).
  10. P. Marcq, H. Chaté, and P. Manneville, Phys. Rev. Lett. 77, 4003 (1996).
  11. P. Marcq, H. Chaté, and P. Manneville, Phys. Rev. E 55, 2606 (1997).
  12. G. Vichniac, Physica D 10, 96 (1984).
  13. N. Metropolis et al., J. Chem. Phys. 21, 1087 (1953).
  14. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, Oxford, 1999).
  15. G. Perez, F. Sastre, and R. Medina, Physica D 168–169, 318 (2002).
  16. E. N. M. Cirillo, F. R. Nardi, and A. D. Plosa, Phys. Rev. E 64, 057103 (2001).
  17. K. Kaneko, Phys. Rev. Lett. 65, 1391 (1990).
  18. G. Abramson and D. H. Zanette, Phys. Rev. E 58, 4454 (1998).
  19. S. Sinha, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 663 (2002).
  20. F. Sastre and G. Pérez, Phys. Rev. E 64, 016207 (2001).
  21. S. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. E 52, 1377 (1995).
  22. K. Binder, Z. Phys. B: Condens. Matter 43, 119 (1981).
  23. D. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000).
  24. J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65, 137 (1990); Phys. Rev. B 43, 3265 (1991).
  25. Finite-Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).
  26. A. M. Ferrenberg and D. P. Landau, Phys. Rev. B 44, 5081 (1991).
  27. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
  28. S. Lepri and W. Just, J. Phys. A 31, 6175 (1998).
  29. F. Sastre and G. Perez, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 251 (2000).

Outline

Information

Phys. Rev. E 71, 036228– Published 31 March, 2005
  • Received 16 April 2004

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation