A Monte Carlo study of the spinless Falicov-Kimball model in the perturbative regime: preliminary results

Finite-temperature properties of the Falicov-Kimball model on the square lattice have been studied in the perturbative regime, i.e. in the case: 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, and partially in the fourth-order, where it constitutes the Ising model with more complicated frustrated antiferromagnetic interactions. The Monte Carlo method was employed, which proved its accuracy in recent analyses of other spin models, like Ashkin-Teller model. To determine the type of ordering and phase boundaries, the behavior of Binder cumulants, based on the order parameters under consideration, was analyzed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)