The European Physical Journal Special Topics

, Volume 143, Issue 1, pp 273–275 | Cite as

Phase separation of the Potts model in the square lattice

  • M. Ibáñez de Berganza
  • E. E. Ferrero
  • S. A. Cannas
  • V. Loreto
  • A. Petri


When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.


EUROPEAN Physical Journal Special Topic Ground State Energy Ginzburg Landau Equation Nonzero Temperature Glauber Dynamic 
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  1. I.M. Lifshitz, Zh. Eksp. Teor. Fiz. 42 (1962); Sov. Phys. JEPT 15, 939 (1962) Google Scholar
  2. S.M. Allen, J.W. Cahn, Acta Metall. 27, 1085 (1979) CrossRefGoogle Scholar
  3. A.J. Bray, Adv. Phys. 43, 357 (1994) CrossRefADSMathSciNetGoogle Scholar
  4. J.D. Gunton, M. San Miguel, P. Sahni, Phase Transitions and Critical Phenomena, edited by C. Domb and J.L. Lebowitz (Academic, London, 1983) 8, 267 and references therein Google Scholar
  5. See references 18–26 of Grest88 Google Scholar
  6. G.S. Grest, M.P. Anderson, Phys. Rev. B 38, 4752 (1988) CrossRefADSGoogle Scholar
  7. M. Ibáñez de Berganza, V. Loreto, A. Petri, Philosophical Magazine, Special Issue: “X International Workshop on Disordered Systems” (2006) (preprint) cond-mat/0606282 Google Scholar
  8. F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982) CrossRefADSGoogle Scholar
  9. C. Jeppesen, O.G. Mouritsen, Phys. Rev. B 47, 14724 (1993) CrossRefADSGoogle Scholar
  10. C. Sire, S.N. Majumdar, Phys. Rev. Lett. 74, 004321 (1995) CrossRefADSGoogle Scholar
  11. See references 1–17 of Grest88 Google Scholar
  12. M. Lau, C. Dasgupta, O.T. Valls, Phys. Rev. B 38, 9024 (1988) CrossRefADSGoogle Scholar
  13. M.J. de Oliveira, A. Petri, T. Tomé, Europhys. Lett. 65, 20 (2004) CrossRefADSGoogle Scholar
  14. M.J. de Oliveira, A. Petri, T. Tomé, Physica A 342, 97–103 (2004); A. Petri, Braz. J. Phys. 33, 521 (2003) CrossRefADSGoogle Scholar
  15. M. Ibáñez de Berganza, E. Ferrero, S. Cannas, V. Loreto, A. Petri, “Slow dynamics of the Potts ferromagnet at low temperature” (to be published) Google Scholar
  16. F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982) CrossRefADSGoogle Scholar
  17. R.J. Baxter, J. Phys. C 6, L445 (1973) Google Scholar
  18. V. Spirin, P.L. Krapivsky, S. Redner, Phys. Rev. E 65, 016119 (2001) CrossRefADSGoogle Scholar
  19. C. Godrèche, J.M. Luck, J. Phys.: Condens. Matter 17, S2573 (2005) and references therein Google Scholar
  20. P. Derrida, P.M.C. De Oliveira, D. Stauffer, Physica A 224, 604 (1996) CrossRefADSMathSciNetGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • M. Ibáñez de Berganza
    • 1
  • E. E. Ferrero
    • 2
  • S. A. Cannas
    • 2
  • V. Loreto
    • 1
  • A. Petri
    • 3
  1. 1.Dipartimento di FisicaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad UniversitariaCórdobaArgentina
  3. 3.CNR, Istituto dei Sistemi Complessi, Sede di Roma 2-Tor Vegata, via del Fosso del Cavaliere 100RomaItaly

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