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Universal Amplitude Ratios for the 3-state and 4-state Potts models

Universal Amplitude Ratios for the 3-state and 4-state Potts models. Lev N. Shchur , Landau Institute for Theoretical Physics, Chernogolovka, Russia. Universal Amplitude Ratios for the 3-state and 4-state Potts models. Starring:. Bertrand Berche,

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Universal Amplitude Ratios for the 3-state and 4-state Potts models

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  1. Universal Amplitude Ratios for the 3-state and 4-state Potts models Lev N. Shchur, Landau Institute for Theoretical Physics, Chernogolovka, Russia

  2. Universal Amplitude Ratios for the 3-state and 4-state Potts models Starring: Bertrand Berche, Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy 1, France “Monsiuer” Republican

  3. Universal Amplitude Ratios for the 3-state and 4-state Potts models Starring: Paolo Butera, Istituto Nazionale di Fisica Nucleare, Sezione di Milano-Bicocca, Italy “Signore Milanese”

  4. Universal Amplitude Ratios for the 3-state and 4-state Potts models Special Guest: Special Host: Wolfhard Janke, Universitat Leipzig, Germany “Richtig Deutsch” – 100% Fat free – 100%, Sugar free – 100%, …

  5. Universal Amplitude Ratios for the 3-state and 4-state Potts models Acknowledgments: Walter Selke Malte Henkel Ference Igloi V. Plechko J. Cardy J. Salas Alexander Zamolodchikov

  6. Critical behavior in the vicinity of critical point

  7. Universal combinations of amplitudes Universality class: dimension, symmetry of ordered phase and number of order parameters

  8. 2-state Potts model (2D Ising model): Onsager 1944 Wu, McCoy, Tracy, Barouch 1976 Delfino 1999

  9. 2D Ising model LS & Vasilyev 2001 0.9625817322… 0.0255369716… Finite size effects

  10. Critical region window

  11. Potts model – MC simulations Binder 1981 LS, Butera, Berche 2002

  12. Potts model – Series Expansions (SE)

  13. q=3 Potts model LS, Butera, Berche 2002 Fit data to the expression

  14. LS, Berche, Butera 2007 q=3,4 Potts model Specific heat

  15. Duality Specific heat Effective amplitudes of Specific Heat as Energy differences

  16. Duality Effective ratio On the dual line At symmetric temperatures

  17. Duality

  18. 3-state Potts model critical amplitude ratios

  19. 4-state Potts model critical behavior Magnetization Fit to effective amplitude

  20. 4-state Potts model critical behavior Effective amplitudes

  21. 4-state Potts model critical behavior Effective amplitudes From Baxter-Wu model (with W.Janke) Delfino-Cardy prediction 4.013 and 0.0204, repsectively

  22. Summary • What we learn: • Appropriate temperature window should be defined • Duality and other analytical considerations may be extremely helpful • Corrections to scaling should be checked • Numerical estimators should be chosen carefully • What we get: • Extremely good estimation of critical amplitudes • Excellent coincidence of results with the analytical predictions • for 3-state Potts model • Disagreement for 4-state Potts model • Support of independent results for Baxter-Wu model • Evidence for the cancellation of the all logarithmic correction • universal amplitude ratios

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