Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 8, 2014

Numerical study of the three-state Ashkin-Teller model with competing dynamics

Prosper Ndizeye EMAIL logo , Felix Hontinfinde , Basile Kounouhewa and Smaine Bekhechi
From the journal Open Physics


An open ferromagnetic Ashkin-Teller model with spin variables 0, ±1 is studied by standard Monte Carlo simulations on a square lattice in the presence of competing Glauber and Kawasaki dynamics. The Kawasaki dynamics simulates spin-exchange processes that continuously flow energy into the system from an external source. Our calculations reveal the presence, in the model, of tricritical points where first order and second order transition lines meet. Beyond that, several self-organized phases are detected when Kawasaki dynamics become dominant. Phase diagrams that comprise phase boundaries and stationary states have been determined in the model parameters’ space. In the case where spin-phonon interactions are incorporated in the model Hamiltonian, numerical results indicate that the paramagnetic phase is stabilized and almost all of the self-organized phases are destroyed.

[1] G. Nicolis, I. Prigogine, Self-oganization in Non-Equilibrium Systems (Wiley, New York, 1977) Search in Google Scholar

[2] A. I. López-Lacomba, J. Marro, Phys. Rev. B 46, 8244 (1992) in Google Scholar PubMed

[3] Liu JiWen, M.A. YuQuiang, Commun. Theor. Phys. (Beijing, China) 32, 305 (1999) 10.1088/0253-6102/32/2/305Search in Google Scholar

[4] P. L. Garrido, J. Marro, Europhys. Lett. 15, 375 (1991) in Google Scholar

[5] P. L. Garrido, J. Marro, J. Phys. A 25, 1453 (1992) in Google Scholar

[6] H. Haken, Synergetics, 3rd ed. (Springer-Verlag, Berlin, 1983) in Google Scholar

[7] B. C. S. Grandi, W. Figueiredo, Phys. Rev. E 56, 5240 (1997) in Google Scholar

[8] F. Hontinfinde, S. Bekhechi, R. Ferrando, Eur. Phys. J. B 16, 681 (2000). in Google Scholar

[9] K. Kawasaki, In Phase Transition and Critical Phenomena, edited by C. Domb, M. S. Green (Academic Press, London 1972), vol. 2. Search in Google Scholar

[10] R. J. Glauber, J. Phys. 4, 294 (1963) 10.1063/1.1703954Search in Google Scholar

[11] T. Tomé, M. J. de Oliveira, Phys. Rev. A 40, 6643 (1989) in Google Scholar PubMed

[12] S. Bekhechi, A. Benyoussef, B. Ettaki, M. Loulidi, A. El Kenz, F. Hontinfinde, Phys. Rev. E 64, 016134 (2001) in Google Scholar PubMed

[13] J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943) in Google Scholar

[14] A. B. Bortz, M. H. Kalos, J. L. Lebowitz, J. Comput. Phys. 17, 10 (1975) in Google Scholar

[15] M. Blume, V. J. Emery, R. B. Griffiths, Phys. Rev. A 4, 1071 (1971) in Google Scholar

[16] T. D. Oke, F. Hontinfinde, K. Boukheddaden, Eur. Phys. J. B 86, 271 (2013) in Google Scholar

Published Online: 2014-5-8
Published in Print: 2014-5-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 5.12.2022 from
Scroll Up Arrow