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physica status solidi (b)

Pattern formation in the Falicov–Kimball model

Maciej M. Maśka, Katarzyna Czajka

Published Jan 24, 2005• 28 citations
Publisher

Abstract

Abstract It is known that in the ground state of half‐filled Falicov–Kimball model immobile particles form a checkerboard pattern. On the other hand, there is a wide range of model parameters, for which this model is expected to exhibit a phase separation. Using Monte Carlo simulations we demonstrate how the system reaches these states, as the temperature is lowered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200460067

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Stripes and phase separation in strongly correlated systems

Katarzyna Czajka, Maciej M. Maśka

Abstract Using classical Monte Carlo approach we analyze two‐dimensional Falicov–Kimball model away from half‐filling. Both the weak and the strong interaction regimes are considered. We found that in the former case stripe configurations are the stable ones, whereas in the latter case the phase separation minimize the energy. We present also the spectral properties of the system. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)•May 7, 2007•7 citations

Ground‐state properties of the three‐dimensional Falicov‐Kimball model

Pavol Farkašovský, Hana Čenčariková, Natália Tomašovičová

Abstract The ground‐state properties of the three‐dimensional spinless Falicov‐Kimball model are studied by a wellcontrolled numerical method. The results obtained are used to categorize the ground‐state configurations according to common features for weak, intermediate and strong interactions. It is shown that only a few configuration types form the basic structure of the phase diagram. In particular, the largest regions of stability correspond to phase segregated configurations, striped configurations and configurations in which electrons are distributed in diagonal planes with incomplete chessboard structure. Near half‐filling, mixtures of two phases with complete and incomplete chessboard structure are determined. In addition, the picture of metal‐insulator transitions is presented. The relevance of these results for a description of real material is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•Jan 1, 2006•1 citation

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

Jacek Wojtkiewicz, Grzegorz Musiał, L. Dębski

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)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•Jan 1, 2006•4 citations

Phase transitions in the Falicov–Kimball model away from half-filling

Martin Žonda

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ c , changes to a different ordered phase and at the temperature, that can be several times higher than τ c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.

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Monte Carlo study of the Falicov–Kimball model: implementation of the histogram method

Maciej Wróbel, Mateusz Małczak, Marcin Mierzejewski +1 more

Abstract We show that the histogram method that is widely used in the Monte Carlo simulations for the Ising model, can also be implemented in the simulations carried out for the Falicov–Kimball model. We estimate the systematic errors arising from application of this method and discuss the regimes of model parameters, where these errors are minimal. We apply the histogram method for determining the transition temperature and demonstrate significant advantages over standard simulations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)•Apr 3, 2009•0 citations

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

L. Dębski

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.

Phase Transitions•Oct 19, 2015•5 citations
Abstract It is known that in the ground state of half‐filled Falicov–Kimball model immobile particles form a checkerboard pattern. On the other hand, there is a wide range of model parameters, for which this model is expected to exhibit a phase separation. Using Monte Carlo simulations we demonstrate how the system reaches these states, as the temperature is lowered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract The ground‐state properties of the three‐dimensional spinless Falicov‐Kimball model are studied by a wellcontrolled numerical method. The results obtained are used to categorize the ground‐state configurations according to common features for weak, intermediate and strong interactions. It is shown that only a few configuration types form the basic structure of the phase diagram. In particular, the largest regions of stability correspond to phase segregated configurations, striped configurations and configurations in which electrons are distributed in diagonal planes with incomplete chessboard structure. Near half‐filling, mixtures of two phases with complete and incomplete chessboard structure are determined. In addition, the picture of metal‐insulator transitions is presented. The relevance of these results for a description of real material is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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)
The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ c , changes to a different ordered phase and at the temperature, that can be several times higher than τ c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.
Abstract We show that the histogram method that is widely used in the Monte Carlo simulations for the Ising model, can also be implemented in the simulations carried out for the Falicov–Kimball model. We estimate the systematic errors arising from application of this method and discuss the regimes of model parameters, where these errors are minimal. We apply the histogram method for determining the transition temperature and demonstrate significant advantages over standard simulations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.