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Arbitrarily Weak First Order Phase Transitions in the 3D Standard Ashkin-Teller Model by MC Computer Experiments

100%
Jeziorek-Knioła D., Musiał G., Wojtkowiak Z.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
327-329
EN
The first order phase transition line in the vicinity of the tricritical Ising point region is studied in the 3D standard Ashkin-Teller model on a cubic lattice. The large-scale Monte Carlo computer experiments using the Binder- and Challa-like cumulants, the latter modified by Musial, are proposed and performed. Specific behavior of the Challa-Musial cumulants for weak first order phase transitions is discovered and its interpretation is proposed. The paper proves the arbitrarily weak first order character of phase transitions when approaching to the Ising point.
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Computation of Latent Heat based on the Energy Distribution Histogram in the 3D Ashkin-Teller Model

100%
Jeziorek-Knioła D., Wojtkowiak Z., Musiał G.
Acta Physica Polonica A
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2018
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vol. 133
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issue 3
435-437
EN
The method of computation of the latent heat based on the energy distribution histogram is applied to the standard 3D Ashkin-Teller (AT) model. Similarly as in the original method for the q-state Potts model for strong first order phase transitions, the characteristic histogram with two peaks in the critical region have been observed. Positions of two minima of negative logarithm of internal energy probability for samples of finite size show good linear scalability to the thermodynamic limit. The applicability of this method has been confirmed by proving that the latent heat values are consistent with the ones obtained by us using the analysis of the behavior of the cumulants of the type of Challa and of Lee-Kosterlitz. The presented method is far more efficient than the one based on those cumulants.
3
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On Non-Ising Phase Transitions in the 3D Standard Ashkin-Teller Model

88%
Jeziorek-Knioła D., Musiał G., Dębski L., Rogiers J., Dylak S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1105-1107
EN
The phase transition line near the Ising point region is studied for the 3D standard Ashkin-Teller model on a cubic lattice. This model with a multicomponent order parameter is one of the important reference points in statistical physics since it shows an interesting and complicated phase diagram. The main motivation for our study was nonuniversal behavior suggested for this line. The large-scale Monte Carlo simulations using the Binder and Challa like cumulants are performed. Accurate analysis to exclude the latent heat inherence is applied. Specific behavior of the Challa like cumulants is discovered and its interpretation is proposed. The paper is closed with preliminary conclusions concerning the continuous but non-Ising character of these phase transitions in the lower part of the mixed phase region and the possiblity of the first order on the line connecting it to the Ising point.
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