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Phase Transitions

The possibility of detection of finite temperature stripe ordering in 2D spinless Falicov–Kimball model

L. Dębski

Published Oct 19, 2015• 5 citations
Publisher

Abstract

This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.

DOI
10.1080/01411594.2015.1080257

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This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.
Finite-temperature properties of the Falicov-Kimball model in two approximations were studied in the perturbative regime, i.e. for t/U 1, where t = 1 is the hopping constant and U = 10 denotes the Coulomb interaction strength.In our study, we determined the phase diagram of the model in the second order of the perturbation theory, where it reduces to the antiferromagnetic Ising model in the emergent magnetic field.In the fourth order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the phase diagram was established.The Monte Carlo method was employed to investigate the phase transition lines.The existence of stripe ordering at finite temperatures is proved.
Abstract 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)
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.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.