The spin-dependent Falicov-Kimball model (FKM) is studied on a triangular lattice using numerical diagonalization technique and Monte-Carlo simulation algorithm. Magnetic properties have been explored for different values of parameters: on-site Coulo
mb correlation $U$, exchange interaction $J$ and filling of electrons. We have found that the ground state configurations exhibit long range Ne`el order, ferromagnetism or a mixture of both as $J$ is varied. The magnetic moments of itinerant ($d$) and localized ($f$) electrons are also studied. For the one-fourth filling case we found no magnetic moment from $d$- and $f$-electrons for $U$ less than a critical value.
A numerical diagonalization technique with canonical Monte-Carlo simulation algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a triangular
lattice with correlated hopping ($t^{prime}$). It is observed that the low temperature ordered phases (i.e. regular, bounded and segregated) persist up to a finite critical temperature ($T_{c}$). In addition, we observe that the critical temperature decreases with increasing the correlated hopping in regular and bounded phases whereas it increases in the segregated phase. Single and multi peak patterns seen in the temperature dependence of specific heat ($C_v$) and charge susceptibility ($chi$) for different values of parameters like on-site Coulomb correlation strength ($U$), correlated hopping ($t^{prime}$) and filling of localized electrons ($n_{f}$) are also discussed.
Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite tempera
ture. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (C_v) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f-electron energy (E_f) and temperature.
