Skip to main content
SpringerLink
Log in

Critical behavior and out-of-equilibrium dynamics of a two-dimensional Ising model with dynamic couplings

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest neighbors of each spin pair, which prevents the system from ordering in a full ferromagnetic or antiferromagnetic state. Using a parallel-tempering Monte Carlo algorithm, we find that the model undergoes a continuous phase transition at finite temperature, which belongs to the Ising universality class. The properties of the bond structure and the ground-state entropy are also studied. Finally, we analyze the out-of-equilibrium dynamics which displays typical glassy characteristics at a temperature well below the critical one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Binder, A.P. Young, Rev. Mod. Phys. 58, 801 (1986)

    Article  ADS  Google Scholar 

  2. M.E.J. Newman, C. Moore, Phys. Rev. E 60, 5068 (1999)

    Article  ADS  Google Scholar 

  3. A. Lipowski, J. Phys. A 30, 7365 (1997)

    Article  ADS  MATH  Google Scholar 

  4. M.R. Swift, H. Bokil, R.D.M. Travasso, A. Bray, Phys. Rev. B 62, 11494 (2000)

    Article  ADS  Google Scholar 

  5. A. Buhot, J.P. Garrahan, Phys. Rev. Lett. 88, 225702 (2002)

    Article  ADS  Google Scholar 

  6. A. Cavagna, I. Giardina, T.S. Grigera, J. Chem. Phys. 118, 6974 (2003)

    Article  ADS  Google Scholar 

  7. G. Biroli, M. Mezard, Phys. Rev. Lett. 88, 025501 (2001)

    Article  ADS  Google Scholar 

  8. F. Krzakala, M. Tarzia, L. Zdeborová, Phys. Rev. Lett. 101, 165702 (2008)

    Article  ADS  Google Scholar 

  9. P. Lazić, D.K. Sunko, Eur. Phys. J. B 21, 595 (2001)

    Article  ADS  Google Scholar 

  10. S.F. Edwards, P.W. Anderson, J. Phys. F 5, 965 (1975)

    Article  ADS  Google Scholar 

  11. G. Toulouse, Commun. Phys. 2, 115 (1977)

    Google Scholar 

  12. A.K. Hartmann, Phys. Rev. B 67, 214404 (2003)

    Article  ADS  Google Scholar 

  13. A. Fierro, Phys. Rev. E 70, 012501 (2004)

    Article  ADS  Google Scholar 

  14. C.J. Geyer, in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface (American Statistical Association, New York, 1991), p. 156

  15. K. Hukushima, K. Nemoto, Phys. Soc. Jpn 65, 1604 (1996)

    Article  ADS  Google Scholar 

  16. N. Metropolis, A.W. Rosenbluth, N.M. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  17. A.K. Hartmann, H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Berlin, 2001)

  18. D.J. Earl, M.W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005)

    Article  Google Scholar 

  19. H.G. Katzgraber, S. Trebst, D.A. Huse, M. Troyer, J. Stat. Mech. 2006, P03018 (2006)

    Article  Google Scholar 

  20. D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, UK, 2005)

  21. K. Binder, in Applications of the Monte Carlo Method in Statistical Physics, Topics in current Physics (Springer, Berlin, 1984), Vol. 36

  22. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1995)

  23. C. Chatelain, J. Phys. A 36, 10739 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. F. Ricci-Tersenghi, Phys. Rev. E 68, 065104R (2003)

    Article  ADS  Google Scholar 

  25. L.F. Cugliandolo, J. Kurchan, J. Phys. A 27, 5749 (1994)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. A. Crisanti, F. Ritort, J. Phys. A 36, R181 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  27. H.G. Katzgraber, M. Körner, A.P. Young, Phys. Rev. B 73, 224432 (2006)

    Article  ADS  Google Scholar 

  28. K. Binder, D.P. Landau, Phys. Rev. B 30, 1477 (1984)

    Article  ADS  Google Scholar 

  29. M.S.S. Challa, D.P. Landau, K. Binder, Phys. Rev. B 34, 1841 (1986)

    Article  ADS  Google Scholar 

  30. K. Vollmayr, J.D. Reger, M. Scheucher, K. Binder, Z. Phys. B 91, 113 (1993)

    Article  ADS  Google Scholar 

  31. M.E. Fisher, Critical Phenomena (Academic Press, London, 1971)

  32. V. Privman, Finite Size Scaling and Numerical Simulation of Statistical Systems (World Scientific, Singapore, 1990)

  33. A.M. Ferrenberg, D.P. Landau, Phys. Rev. B 44, 5081 (1991)

    Article  ADS  Google Scholar 

  34. W. Janke, M. Katoot, R. Villanova, Phys. Rev. B 49, 9644 (1994)

    Article  ADS  Google Scholar 

  35. K. Binder, E. Luijten, Phys. Rep. 344, 179 (2001)

    Article  ADS  MATH  Google Scholar 

  36. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971)

  37. F. Romá, F. Nieto, E.E. Vogel, A.J. Ramirez-Pastor, J. Stat. Phys. 114, 1325 (2004)

    Article  ADS  MATH  Google Scholar 

  38. S. Kirkpatrick, Phys. Rev. B 16, 4630 (1977)

    Article  ADS  Google Scholar 

  39. K. Binder, J. Comput. Phys. 59, 1 (1985)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. D.J. Perez-Morelo, A.J. Ramirez-Pastor, F. Romá, Physica A 391, 937 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  41. K. Saul, M. Kardar, Nucl. Phys. B 432, 641 (1994)

    Article  ADS  Google Scholar 

  42. J.S. Zhan, L.W. Lee, Physica A 295, 239 (2000)

    Article  ADS  Google Scholar 

  43. A.K. Hartmann, Phys. Rev. E 63, 016106 (2001)

    Article  ADS  Google Scholar 

  44. J.L. Moreno, H.G. Katzgraber, A.K. Hartmann, Int. J. Mod. Phys. C 14, 285 (2003)

    Article  ADS  Google Scholar 

  45. F. Romá, S. Risau-Gusman, A.J. Ramirez-Pastor, F. Nieto, E.E. Vogel, Physica A 388, 2821 (2009)

    Article  ADS  Google Scholar 

  46. L. Berthier, G. Biroli, Rev. Mod. Phys. 83, 587 (2011)

    Article  ADS  Google Scholar 

  47. G. Parisi, Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter (Springer, Berlin, 2003)

  48. L. Onsager, Phys. Rev. 65, 117 (1944)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  49. F. Romá, A.J. Ramirez-Pastor, J.L. Riccardo, Phys. Rev. B 68, 205407 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Investigaciones y Transferencia de Santiago del Estero (CITSE), Universidad Nacional de Santiago de Estero, CONICET Ruta Nacional 9, Km 1125, Villa el Zanjón, 4206, Santiago del Estero, Argentina

    Oscar A. Pinto

  2. Departamento de Física, Universidad Nacional de San Luis, INFAP, CONICET, Chacabuco 917, D5700BWS, San Luis, Argentina

    Federico Romá

  3. Centro Atómico Bariloche, R8402AGP San Carlos de Bariloche, CONICET, Río Negro, Argentina

    Sebastian Bustingorry

Authors
  1. Oscar A. Pinto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Federico Romá
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastian Bustingorry
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federico Romá.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pinto, O.A., Romá, F. & Bustingorry, S. Critical behavior and out-of-equilibrium dynamics of a two-dimensional Ising model with dynamic couplings. Eur. Phys. J. B 87, 299 (2014). https://doi.org/10.1140/epjb/e2014-50592-3

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50592-3

Keywords

Search

Navigation