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