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The Monte Carlo Computer Experiment to Study the Order and Phase Transitions in the Mixed Phase Region Based on the Example of the 3D Ashkin-Teller Model

Wojtkowiak Z., Musiał G.

Computational Methods in Science and Technology

2021

Vol. 27, No. 3

129--136

In this paper, we demonstrate a new way of performing Monte Carlo (MC) simulations in a mixed phase region that is difficult to study, where with certain probabilities there are different ordering ways. That results in a large oscillation of the values of the computed thermodynamic quantities, which makes their interpretation very problematic. Our results are presented on the example of the 3D Askin-Teller (AT) model, where within a certain range of parameters with equal probabilities there are two different, but equivalent, ways of ordering two of the three order parameters showing independent behavior. The use of our new approach in an MC computer experiment allowed us to use Binder cumulant as well as Challaand the Lee-Kosterlitz-like cumulants. This made it possible to locate phase transitions precisely enough to be able to use the energy distribution histogram method. According to the most effective strategy in the critical region we use our recently proposed cluster MC algorithm and the Metropolis algorithm beyond it, which are suitable for both the first-order and the continuous phase transitions in the 3D AT model. The new approach was demonstrated by determining smooth curves of magnetization and internal energy, and as a consequence by determining the location and character of the phase transition on the line between the mixed phase region and the paramagnetic phase.

Computation of latent heat in the system of multi-component order parameter : 3D Ashkin-Teller model

Jeziorek-Knioła D., Wojtkowiak Z., Musiał G.

Computational Methods in Science and Technology

2019

Vol. 25, No. 1

31--39

The method for computing the latent heat in a system with many independently behaving components of the order parameter proposed previously is presented for a chosen point of the phase diagram of the 3D Ashkin-Teller (AH) model. Binder, Challa, and Lee-Kosterlitz cumulants are exploited and supplemented by the use of the energy distribution histogram. The proposed computer experiments using the Metropolis algorithm calculate the cumulants in question, the internal energy and its partial contributions as well as the energy distribution for the model Hamiltonian and its components. The important part of our paper is an attempt to validate the results obtained by several independent methods.