Kuantum parçacık sistemlerin renormalizasyon grubu kuramı

The global phase diagram of the spinless Falicov?Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered phases, in which the system forms two sublattices with different electron densities. The charge-ordered phases occur at and near half-filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase separation (phase coexistance) at and near half-filling of both localized and conduction electrons. These coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions, hopping strengths, and temperatures, are calculated and exhibit a multitude of distinct topologies.