Abstract.
The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for charge orderings are obtained. The phase diagrams include three types of charge ordered phases and the nonordered phase. The system exhibits very rich structure and shows unusual multicritical behavior. In the limiting case of tij=0, the EHM is equivalent to the pseudospin model with single-ion anisotropy \(\frac{1}{2}U\), exchange interaction W in an effective magnetic field \({\left( \mu - \frac{1}{2}U - z_{0}W\right) }\). This classical spin model is analyzed using the MC method for the canonical ensemble. The phase diagram is compared with the known results for the Blume-Capel model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.M. Gabovich, A.I. Voitenko, M. Ausloos, Phys. Rep. 367, 583 (2002)
T. Goto, B. Lüthi, Adv. in Phys. 52, 67 (2003)
M.S. Reis, V.S. Amaral, J.P. Araujo, P.B. Tavares, A.M. Gomes, I.S. Oliveira, Phys. Rev. B 71, 144413 (2005)
S. Robaszkiewicz, Phys. Stat. Sol. (b) 59, K63 (1973); S. Robaszkiewicz, Acta. Phys. Pol. A 45, 289 (1974)
Duc Anh Le, Anh Tuan Hoang, Toan Thang Nguyen, Mod. Phys. Lett. B 17, Nos. 20, 21, 1103 (2003)
K. Rościszewski, A. Oleś, J. Phys.: Condens. Matt. 15, 8363 (2003)
M. Aichhorn, H.G. Evertz, W. von der Linden, M. Potthoff, Phys. Rev. B 70, 235107 (2004)
Y.Z. Zhang, Tran Minh-Tien, V. Yushankhai, P. Thalmeier, Eur. Phys. J. B 44, 265 (2005)
A.T. Hoang, P. Thalmeier, J. Phys.: Condens. Matter 14, 6639 (2002)
N.-H. Tong, S.-Q. Shen, R. Bulla, Phys. Rev. B 70, 085118 (2004)
S. Onari, R. Arita, K. Kuroki, H. Aoki, Phys. Rev. B 70, 094523 (2004)
R.A. Bari, Phys. Rev. B 3, 2662 (1971)
D. Ihle, B. Lorenz, Phys. Stat. Sol. (b) 60, 319 (1973)
G. Beni, P. Pincus, Phys. Rev. B 9, 2963 (1974)
R.S. Tu, T.A. Kaplan, Phys. Stat. Sol. (b) 63, 659 (1974)
B. Lorenz, Phys. Stat. Sol. (b) 106, K17 (1981)
T.M. Rice, L. Sneddon, Phys. Rev. Lett. 47 689 (1981)
S. Robaszkiewicz, T. Kostyrko, Physica B & C 112, 389 (1982)
R. Micnas, S. Robaszkiewicz, K.A. Chao, Phys. Rev. B 29, 2784 (1984)
R.J. Bursill, C.J. Thompson, J. Phys. A: Math. Gen. 26, 4497 (1993)
J. Jędrzejewski, Physica A 205, 702 (1994)
M. Bartkowiak, J.A. Henderson, J. Oitmaa, P.E. de Brito, Phys. Rev. B 51, 14077 (1995)
C. Borgs, J. Jędrzejewski, R. Kotecky, J. Phys. A: Math. Gen. 29, 733 (1996)
E. Halvorsen, M. Bartkowiak, Phys. Rev B 63, 014403 (2000)
F. Mancini, Eur. Phys. J. B 47, 527 (2005)
D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge 2000)
D. Loison, C.L. Qin, K.D. Schotte, X.F Jin, Eur. Phys. J B 41, 395 (2004)
K. Binder, D.P. Landau, Phys. Rev. B 21, 1941 (1980)
J.D. Kimel, S. Black, P. Carter, Yung-Li Wang, Phys. Rev. B 35, 3347 (1987)
J.D. Kimel, Per Arne Rikvold, Yung-Li Wang, Phys. Rev. B 45, 7237 (1992)
The results for ferromagnetic BC model: J.C. Xavier, F.C. Alcaraz, D. Pena Lara, J.A. Plascak, Phys. Rev. B 57, 11575 (1998); C.J. Silva, A.A. Caparica, J.A. Plascak, Phys. Rev. E 73, 036702 (2006)
J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976)
G. Pawłowski, Phys. Stat. Solidi (b) 243, 331 (2006)
S. Kirkpatrick, in III-Condensed Matter, edited by R. Balian, R. Maynard, G. Toulouse (North-Holland, Amsterdam 1979), p. 321
S. Robaszkiewicz, private communication; see also: Acta. Phys. Pol. A 85, 117 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pawłowski, G. Charge orderings in the atomic limit of the extended Hubbard model. Eur. Phys. J. B 53, 471–479 (2006). https://doi.org/10.1140/epjb/e2006-00409-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00409-1