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

• Authors: Prosper Ndizeye , Felix Hontinfinde , Basile Kounouhewa , Smaine Bekhechi
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

The Ashkin-Teller model; Kawasaki and Glauber dynamics; Monte Carlo simulations; self-organization; tricritical point

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 5
• Pages: 375-382

Dates

published

1 - 5 - 2014

online

8 - 5 - 2014

Contributors

author

Prosper Ndizeye

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Benin

author

Felix Hontinfinde

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Benin

author

Basile Kounouhewa

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Benin

author

Smaine Bekhechi

• Laboratoire de Physique Théorique, Département de Physique, Université Abou Bakr Belkaid, Tlemcen, Algérie

References

• [1] G. Nicolis, I. Prigogine, Self-oganization in Non-Equilibrium Systems (Wiley, New York, 1977)
• [2] A. I. López-Lacomba, J. Marro, Phys. Rev. B 46, 8244 (1992) http://dx.doi.org/10.1103/PhysRevB.46.8244[Crossref]
• [3] Liu JiWen, M.A. YuQuiang, Commun. Theor. Phys. (Beijing, China) 32, 305 (1999)
• [4] P. L. Garrido, J. Marro, Europhys. Lett. 15, 375 (1991) http://dx.doi.org/10.1209/0295-5075/15/4/002[Crossref]
• [5] P. L. Garrido, J. Marro, J. Phys. A 25, 1453 (1992) http://dx.doi.org/10.1088/0305-4470/25/6/008[Crossref]
• [6] H. Haken, Synergetics, 3rd ed. (Springer-Verlag, Berlin, 1983) http://dx.doi.org/10.1007/978-3-642-88338-5[Crossref]
• [7] B. C. S. Grandi, W. Figueiredo, Phys. Rev. E 56, 5240 (1997) http://dx.doi.org/10.1103/PhysRevE.56.5240[Crossref]
• [8] F. Hontinfinde, S. Bekhechi, R. Ferrando, Eur. Phys. J. B 16, 681 (2000). http://dx.doi.org/10.1007/s100510070186[Crossref]
• [9] K. Kawasaki, In Phase Transition and Critical Phenomena, edited by C. Domb, M. S. Green (Academic Press, London 1972), vol. 2.
• [10] R. J. Glauber, J. Phys. 4, 294 (1963)
• [11] T. Tomé, M. J. de Oliveira, Phys. Rev. A 40, 6643 (1989) http://dx.doi.org/10.1103/PhysRevA.40.6643[Crossref]
• [12] S. Bekhechi, A. Benyoussef, B. Ettaki, M. Loulidi, A. El Kenz, F. Hontinfinde, Phys. Rev. E 64, 016134 (2001) http://dx.doi.org/10.1103/PhysRevE.64.016134[Crossref]
• [13] J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943) http://dx.doi.org/10.1103/PhysRev.64.178[Crossref]
• [14] A. B. Bortz, M. H. Kalos, J. L. Lebowitz, J. Comput. Phys. 17, 10 (1975) http://dx.doi.org/10.1016/0021-9991(75)90060-1[Crossref]
• [15] M. Blume, V. J. Emery, R. B. Griffiths, Phys. Rev. A 4, 1071 (1971) http://dx.doi.org/10.1103/PhysRevA.4.1071[Crossref]
• [16] T. D. Oke, F. Hontinfinde, K. Boukheddaden, Eur. Phys. J. B 86, 271 (2013) http://dx.doi.org/10.1140/epjb/e2013-30801-5[Crossref]

Identifiers

DOI

10.2478/s11534-014-0446-y