Abstract
Within a mean-field approach, the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field is studied. The Glauber-type stochastic dynamics is used to describe the time evolution of the system and obtain the mean-field dynamic equation of motion. The dynamic phase-transition points are calculated and phase diagrams are presented in the temperature and crystal-field interaction plane. According to the values of the magnetic field amplitude, three fundamental types of phase diagrams are found: One exhibits a dynamic tricritical point, while the other two exhibit a dynamic zero-temperature critical point.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. E. Stanley, Introduction to the Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971; Mir, Moscow, 1973); S. Ma, Modern Theory of Critical Phenomena (Benjamin, Reading, Mass., 1976; Mir, Moscow, 1980).
T. Tomé and M. J. de Oliveira, Phys. Rev. A 41, 4251 (1990).
J. F. F. Mendes and E. J. S. Lage, J. Stat. Phys. 64, 653 (1991).
R. J. Glauber, J. Math. Phys. 4, 294 (1963).
M. Acharyya, Phys. Rev. E 56, 2407 (1997); A. Chatterjee and B. K. Chakrabarti, Phys. Rev. E 67, 046113 (2003).
S. W. Sides, P. A. Rikvold, and M. A. Novotny, Phys. Rev. Lett. 81, 834 (1998); Phys. Rev. E 59, 2710 (1999); G. Korniss, C. J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 63, 016120 (2001); G. Korniss, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 66, 056127 (2002).
B. K. Chakrabarti and M. Acharyya, Rev. Mod. Phys. 71, 847 (1999); M. Acharyya, Int. J. Mod. Phys. C 16, 1631 (2005).
A. Krawiecki, Int. J. Mod. Phys. B 19, 4769 (2005).
M. F. Zimmer, Phys. Rev. E 47, 3950 (1993); M. Acharyya and B. K. Chakrabarti, Phys. Rev. B 52, 6550 (1995); M. Acharyya, Phys. Rev. E 58, 179 (1998); H. Fujisaka, H. Tutu, and P. A. Rikvold, Phys. Rev. E 63, 036109 (2001).
H. Tutu and N. Fujiwara, J. Phys. Soc. Jpn. 73, 2680 (2004).
M. Khorrami and A. Aghamohammadi, Phys. Rev. E 65, 056129 (2002).
H. Jang and M. J. Grimson, Phys. Rev. E 63, 066119 (2001); H. Jang, M. J. Grimson, and C. K. Hall, Phys. Rev. B 67, 094411 (2003); Phys. Rev. E 68, 046115 (2003); Z. Huang, Z. Chen, F. Zhang, and Y. Du, Phys. Lett. A 338, 485 (2005).
T. Yasui, H. Tutu, M. Yamamoto, and H. Fujisaka, Phys. Rev. E 66, 036123 (2002).
E. Machado, G. M. Buendía, P. A. Rikvold, and R. M. Ziff, Phys. Rev. E 71, 016120 (2005).
G. M. Buendía and E. Machado, Phys. Rev. E 58, 1260 (1998).
M. Keskin, O. Canko, and E. Kantar, Int. J. Mod. Phys. C 17, 1239 (2006); O. Canko, Ü. Temizer, and M. Keskin, Int. J. Mod. Phys. C 17, 1717 (2006).
M. Keskin, O. Canko, and B. Deviren, Phys. Rev. E 74, 011110 (2006); O. Canko, B. Deviren, and M. Keskin, J. Phys.: Condens. Matter 18, 6635 (2006); M. Keskin, O. Canko, and M. Kirak, J. Stat. Phys. 127, 359 (2007).
Q. Jiang, H. N. Yang, and G. C. Wang, Phys. Rev. B 52, 14911 (1995); J. Appl. Phys. 79, 5122 (1996).
W. Kleemann, T. Braun, J. Dec, and O. Petracic, Phase Transit. 78, 811 (2005).
M. Keskin, O. Canko, and Ü. Temizer, Phys. Rev. E 72, 036125 (2005).
M. Blume, Phys. Rev. 141, 517 (1966).
H. W. Capel, Physica (Utrecht) 32, 966 (1966); 33, 295 (1967).
S. Grollau, E. Kierlik, M. L. Rosinberg, and G. Tarjus, Phys. Rev. E 63, 41111 (2001); A. Du, Y. Q. Yü, and H. J. Liu, Physica A (Amsterdam) 320, 387 (2003); C. Ekiz, Phys. Lett. A 324, 114 (2004).
T. Fiig, B. M. Gorman, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 50, 1930 (1994).
F. Manzo and E. Olivieri, J. Stat. Phys. 104, 1029 (2001).
C. Ekiz, M. Keskin, and O. Yalçin, Physica A (Amsterdam) 293, 215 (2001).
R. Kikuchi, Suppl. Prog. Theor. Phys. 35, 1 (1966).
Author information
Authors and Affiliations
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Keskin, M., Canko, O. & Temizer, Ü. Dynamic phase transition in the kinetic spin-1 Blume-Capel model: Phase diagrams in the temperature and crystal-field interaction plane. J. Exp. Theor. Phys. 104, 936–942 (2007). https://doi.org/10.1134/S1063776107060118
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1063776107060118