Three-state cyclic voter model extended with Potts energy

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 3, 2002, Pages

  Szabó, György ^a   Szolnoki, Attila ^a  

^a RESEARCH INSTITUTE FOR TECHNICAL PHYSICS AND MATERIALS SCIENCE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY; SURFACE ROUGHNESS; SURFACE TENSION;

CYCLIC DOMINANCE; INVERSE TEMPERATURE; POTTS ENERGY; VORTEX DENSITY;

INTERFACIAL ENERGY;

EID: 41349123220     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.036115     Document Type: Article

References (27)

1. R.J. Field and M. Burger, Oscillations and Traveling Waves in Chemical Systems (Wiley Interscience, New York, 1985).
2. M. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
3. J. Maynard Smith, Evolution and Theory of Games (Cambridge University Press, Cambridge, 1982).
4. A.J. Lotka, Proc. Natl. Acad. Sci. U.S.A. 6, 410 (1920);V. Volterra, Leçon sur la Theorie Mathematique de la Lutte pour le Vie (Gauthier-Villars, Paris, 1931).
5. L. Frachebourg, P.L. Krapivsky, and E. Ben-Naim, Phys. Rev. E 54, 6186 (1996).
6. E. Ben-Naim, L. Frachebourg, and P.L. Krapivsky, Phys. Rev. E 53, 3078 (1996).
7. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, England, 1998).
8. K. Tainaka and Y. Itoh, Europhys. Lett. 15, 399 (1991).
9. K. Tainaka, Phys. Rev. E 50, 3401 (1994).
10. G. Szabó, M.A. Santos, and J.F.F. Mendes, Phys. Rev. E 60, 3776 (1999).
11. J. Maynard Smith, Nature (London) 280, 445 (1979).
12. M.C. Boerlist and P. Hogeweg, Physica D 48, 17 (1991).
13. G. Szabó and T. Czárán, Phys. Rev. E 63, 061904 (2001).
14. G. Szabó and M.A. Santos, Phys. Rev. E 59, R2509 (1999).
15. P. Clifford and A. Sudbury, Biometrika 60, 581 (1973).
16. R. Holley and T.M. Liggett, Ann. Prob. 3, 643 (1975).
17. J.T. Cox and D. Griffeath, Ann. Prob. 14, 347 (1986).
18. M.J. de Oliveira, J.F.F. Mendes, and M.A. Santos, J. Phys. A 26, 2317 (1993).
19. J.-M. Drouffe and C. Godrèche, J. Phys. A 32, 249 (1999).
20. I. Dornic, H. Chaté, J. Chave, and H. Hinrichsen, Phys. Rev. Lett. 87, 045701 (2001).
21. B. Sandstede and A. Scheel, Phys. Rev. Lett. 86, 171 (2001).
22. O-U. Kheowan, C-K. Chan, V.S. Zykov, O. Rangsiman, and S. Müller, Phys. Rev. E 64, 035201 (2001).
23. R.B. Potts, Proc. Cambridge Philos. Soc. 49, 106 (1952).
24. F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
25. O.G. Mouritsen, in Kinetics of Ordering and Growth at Surfaces, edited by M.G. Lagally (Plenum Press, New York, 1990).
26. K. Binder and D. Stauffer, Phys. Rev. Lett. 33, 1006 (1974);
27. Phys. Rev. Lett.P.S. Sahni, G.S. Grest, M.P. Anderson, and D.J. Srolovitz, 50, 263 (1983).