**Физика Низких Температур: ***Том ***33**, Выпуск **9** (Сентябрь 2007), c. 1045-1048
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### A Monte Carlo study of the Falicov-Kimball model in the perturbative regime

**Grzegorz Musiał**^{1}, Lech Dębski^{1}, and Jacek Wojtkiewicz ^{2}

^{1}Institute of Physics, Adam Mickiewicz University, 85 Umultowska Ul., Poznań 61-614, Poland

E-mail: gmusial@amu.edu.pl; gulf@spin.amu.edu.pl

^{2}Dept. for Math. Methods in Physics, Warsaw University, 74 Hoża Ul., Warszawa 00-682, Poland

E-mail: wjacek@fuw.edu.pl

*Received January 18, 2007, revised April 2, 2007*

**Аннотация**

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;

PACS: 75.10.Hk Classical spin models;

PACS: 75.30.Kz Magnetic phase boundaries;

PACS: 75.40.Mg Numerical simulation studies.

**Ключевые слова: **Monte Carlo simulations, 2D Falicov–Kimball model, perturbation theory.