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 1976Delfino 1999

2-state Potts model (2D Ising model):

Onsager 1944

2D Ising model LS & Vasilyev 2001

0.9625817322…

0.0255369716…

Finite size effects

Critical region window

Binder 1981Potts model – MC simulations

LS, Butera, Berche 2002

Potts model – Series Expansions (SE)

LS, Butera, Berche 2002q=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 4.013 and 0.0204, 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 model3. Disagreement for 4-state Potts model4. Support of independent results for Baxter-Wu model5. Evidence for the cancellation of the all logarithmic correction universal amplitude ratios