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Lecture notes in computer science

Monte Carlo Method with Parallel Computation of Phase Transitions in the Three-Dimensional Ashkin-Teller Model

Grzegorz Musiał, L. Dębski

Published Jan 1, 2002• 9 citations
Publisher
DOI
10.1007/3-540-48086-2_59

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Monte Carlo analysis of the tricritical behavior in a three-dimensional system with a multicomponent order parameter: The Ashkin-Teller model

Grzegorz Musiał

Our Monte Carlo (MC) method has been extended to determine the type of ordering, the character of phase transitions, and positions of the tricritical points in the three-dimensional Ashkin-Teller spin-lattice model on a cubic lattice, which is an example of a system with multicomponent order parameter. The precise and detailed analyses of the system's behavior at the ends of the lines of Ising-like phase transitions are performed and the corrected phase diagram in these regions is presented and discussed. The localizations of the tricritical points are also given. The specific behavior of the Binder cumulant when crossing a bifurcation point has been discovered and interpreted. Some general conclusions on methods of investigation of the critical behavior of a system with a multicomponent order parameter are closing the paper.

Physical Review B•Jan 15, 2004•30 citations
Our Monte Carlo (MC) method has been extended to determine the type of ordering, the character of phase transitions, and positions of the tricritical points in the three-dimensional Ashkin-Teller spin-lattice model on a cubic lattice, which is an example of a system with multicomponent order parameter. The precise and detailed analyses of the system's behavior at the ends of the lines of Ising-like phase transitions are performed and the corrected phase diagram in these regions is presented and discussed. The localizations of the tricritical points are also given. The specific behavior of the Binder cumulant when crossing a bifurcation point has been discovered and interpreted. Some general conclusions on methods of investigation of the critical behavior of a system with a multicomponent order parameter are closing the paper.