Shape dependence of the finite-size scaling limit in a strongly anisotropic \(\mathsf{O(\infty)}\) model

  • S. CaraccioloEmail author
  • A. Gambassi
  • M. Gubinelli
  • A. Pelissetto
Original Paper


We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for numerical finite-size scaling studies of strongly anisotropic systems.


Anisotropy Critical Exponent Scaling Limit Anisotropic Model Anisotropic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.E. Fisher, in Critical Phenomena, International School of Physics "Enrico Fermi", Course LI, edited by M.S. Green (Academic, New York, 1971)Google Scholar
  2. 2.
    M.N. Barber, Finite--Size Scaling, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, Vol. 8 (Academic, London, 1983)Google Scholar
  3. 3.
    Finite-Size Scaling, edited by J.L. Cardy (North-Holland, Amsterdam, 1988)Google Scholar
  4. 4.
    V. Privman, Finite Size Scaling and Numerical Simulation of Statistical Systems (World Scientific, Singapore, 1990)Google Scholar
  5. 5.
    J.G. Brankov, D.M. Danchev, N.S. Tonchev, Theory of Critical Phenomena in Finite-Size Systems (World Scientific, Singapore, 2000)Google Scholar
  6. 6.
    K. Binder, Z. Phys. B 43, 119 (1981)Google Scholar
  7. 7.
    M. Lüscher, P. Weisz, U. Wolff, Nucl. Phys. B 359, 221 (1991)CrossRefGoogle Scholar
  8. 8.
    H.W.J. Blöte, E. Luijten, J.R. Heringa, J. Phys. A 28, 6289 (1995)Google Scholar
  9. 9.
    S. Caracciolo, R.G. Edwards, S.J. Ferreira, A. Pelissetto, A.D. Sokal, Phys. Rev. Lett. 74, 2969 (1995)CrossRefGoogle Scholar
  10. 10.
    S. Caracciolo, R.G. Edwards, A. Pelissetto, A.D. Sokal, Phys. Rev. Lett. 75, 1891 (1995)CrossRefGoogle Scholar
  11. 11.
    M. Hasenbusch, K. Pinn, S. Vinti, Phys. Rev. B 59, 11471 (1999)CrossRefGoogle Scholar
  12. 12.
    H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J.J. Ruiz-Lorenzo, J. Phys. A 32, 1 (1999)CrossRefzbMATHGoogle Scholar
  13. 13.
    H.W.J. Blöte, L.N. Shchur, A.L. Talapov, Int. J. Mod. Phys. C 10, 1137 (1999)CrossRefGoogle Scholar
  14. 14.
    M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. B 63, 214503 (2001)CrossRefGoogle Scholar
  15. 15.
    B. Schmittmann, R.K.P. Zia, Statistical Mechanics of Driven Diffusive Systems, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, Vol. 17 (Academic, London, 1995)Google Scholar
  16. 16.
    J. Marro, R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999)Google Scholar
  17. 17.
    J. Krug, Adv. Phys. 46, 139 (1997)Google Scholar
  18. 18.
    R.M. Hornreich, J. Magn. Magn. Mater. 15-18, 387 (1980)Google Scholar
  19. 19.
    W. Selke, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, Vol. 15 (Academic, London, 1992)Google Scholar
  20. 20.
    M. Pleimling, M. Henkel, Phys. Rev. Lett. 87, 125702 (2001)CrossRefGoogle Scholar
  21. 21.
    H.W. Diehl, Acta Phys. Slov. 52, 271 (2002)Google Scholar
  22. 22.
    A. Aharony, M.E. Fisher, Phys. Rev. B 8, 3323 (1973)CrossRefGoogle Scholar
  23. 23.
    A. Hucht, J. Phys. A 35, L481 (2002)Google Scholar
  24. 24.
    E. Brézin, J. Zinn-Justin, Phys. Rev. B 13, 251 (1976)CrossRefGoogle Scholar
  25. 25.
    S.L. Sondhi, S.M. Girvin, J.P. Carini, D. Shahar, Rev. Mod. Phys. 69, 315 (1997)CrossRefGoogle Scholar
  26. 26.
    M. Henkel, Nucl. Phys. B 641, 405 (2002)CrossRefzbMATHGoogle Scholar
  27. 27.
    S.M. Bhattacharjee, J.F. Nagle, Phys. Rev. A 31, 3199 (1985)CrossRefGoogle Scholar
  28. 28.
    K. Binder, J.S. Wang, J. Stat. Phys. 55, 87 (1989)MathSciNetGoogle Scholar
  29. 29.
    K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991)CrossRefGoogle Scholar
  30. 30.
    K.-t. Leung, Int. J. Mod. Phys. C 3, 367 (1992)zbMATHGoogle Scholar
  31. 31.
    J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3d edn. (Oxford Science Publication, Clarendon Press, Oxford, 1996)Google Scholar
  32. 32.
    M.N. Barber, M.E. Fisher, Ann. Phys. [NY] 77, 1 (1973)Google Scholar
  33. 33.
    E. Brézin, J. Physique 43, 15 (1982)Google Scholar
  34. 34.
    M.E. Fisher, V. Privman, Commun. Math. Phys. 103, 527 (1986)MathSciNetGoogle Scholar
  35. 35.
    J.G. Brankov, N.S. Tonchev, J. Stat. Phys. 52, 143 (1988)MathSciNetzbMATHGoogle Scholar
  36. 36.
    S. Singh, R.K. Pathria, Phys. Rev. B 40, 9238 (1989)CrossRefGoogle Scholar
  37. 37.
    S. Caracciolo, A. Gambassi, M. Gubinelli, A. Pelissetto, Eur. Phys. J. B 20, 255 (2001)Google Scholar
  38. 38.
    H. Chamati, D.M. Dantchev, N.S. Tonchev, Eur. Phys. J. B 14, 307 (2000)CrossRefGoogle Scholar
  39. 39.
    J.M. Borwein, I.J. Zucker, IMA J. Numer. Anal. 12, 519 (1992)MathSciNetzbMATHGoogle Scholar
  40. 40.
    A. Cucchieri, T. Mendes, A. Pelissetto, A.D. Sokal, J. Stat. Phys. 86, 581 (1997)MathSciNetzbMATHGoogle Scholar
  41. 41.
    S. Caracciolo, A. Gambassi, M. Gubinelli, A. Pelissetto, J. Phys. A 36, L315 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • S. Caracciolo
    • 1
    Email author
  • A. Gambassi
    • 2
  • M. Gubinelli
    • 3
  • A. Pelissetto
    • 4
  1. 1.Dipartimento di Fisica and INFNUniversità di Milano, and INFM-NESTMilanoItaly
  2. 2.Dipartimento di Fisica and INFNMax-Planck-Institut für MetallforschungStuttgartGermany
  3. 3.Institut für Theoretische und Angewandte PhysikUniversität StuttgartGermany
  4. 4.Dipartimento di Matematica Applicata and INFNUniversità di PisaPisaItaly

Personalised recommendations