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, Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy 1, France “Monsiuer” Republican

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”

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

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

Critical behavior in the vicinity of critical point

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

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

2D Ising model LS & Vasilyev … … Finite size effects

Critical region window

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

Potts model – Series Expansions (SE)

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

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

Duality Specific heat Effective amplitudes of Specific Heat as Energy differences

Duality Effective ratio On the dual line At symmetric temperatures

Duality

3-state Potts model critical amplitude ratios

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

4-state Potts model critical behavior Effective amplitudes

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

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 3.Disagreement for 4-state Potts model 4.Support of independent results for Baxter-Wu model 5.Evidence for the cancellation of the all logarithmic correction universal amplitude ratios