Abstract
This paper presents a cluster Monte Carlo method suitable for both, the first- and the second-order phase transitions in the 3D Ashkin–Teller (AT) model. A cluster algorithm is necessary to verify correctness of the results obtained so far using Metropolis algorithm exhibiting significant critical slowing down. Moreover, metastable states have recently been investigated in this model which can affect the results, especially obtained using the Metropolis algorithm. Our Wolff type algorithm is described and its dynamic critical behavior is demonstrated. Our computer experiments exploit the properties of Binder and Challa cumulants and additionally the one proposed by Lee and Kosterlitz, the last two adapted by us to give clear results for the AT model. The energy distribution histogram method is also independently applied for the first time for the 3D AT model using the Wolff type algorithm. For validation of the previous results and of our algorithm, it is demonstrated that the results of our computations along the line between Ising and Potts points, which are rescaled to their thermodynamic limits, are consistent with those obtained using the Metropolis algorithm. It is also shown that the presented cluster algorithm of the Wolff type significantly reduces the problem of critical slowing down for the 3D AT model, and the dynamic critical exponent reaches values close to zero. As the best strategy, it is suggested to use the cluster algorithm in the critical region and the Metropolis one beyond.
Published Version
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