Low Temperature Physics: 33, 797 (2007); https://doi.org/10.1063/1.2781508 (3 pages)
Fizika Nizkikh Temperatur: Volume 33, Number 9 (September 2007), p. 1045-1048 ( to contents , go back )
A Monte Carlo study of the Falicov-Kimball model in the perturbative regime
Grzegorz Musiał1, Lech Dębski1, and Jacek Wojtkiewicz 2
1Institute of Physics, Adam Mickiewicz University, 85 Umultowska Ul., Poznań 61-614, Poland
2Dept. for Math. Methods in Physics, Warsaw University, 74 Hoża Ul., Warszawa 00-682, Poland
Received January 18, 2007, revised April 2, 2007
Finite-temperature properties of the Falicov–Kimball model on the square lattice have been studied in the perturbative regime, i.e. for t/U << 1, where t is the hopping constant and U denotes the Coulomb interaction strength. In our study, we have determined the phase diagram of the model in the second-order of the perturbation theory, where the antiferromagnetic Ising model in the magnetic field emerges. In the fourth-order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the sketch of the phase diagram was established. The Monte Carlo method was employed and the behavior of Binder cumulants based on the order parameters was analyzed to determine the type of ordering and phase boundaries in the diagram.
PACS: 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems;
Key words: Monte Carlo simulations, 2D Falicov–Kimball model, perturbation theory.