Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

physica status solidi (b)

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

Maciej Wróbel, Mateusz Małczak, Marcin Mierzejewski, Maciej M. Maśka

Published Apr 3, 2009• 0 citations
Publisher

Abstract

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)

DOI
10.1002/pssb.200881563

Related papers

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

A Monte Carlo study of the Falicov-Kimball model in the perturbative regime

Grzegorz Musiał, L. Dębski, Jacek Wojtkiewicz

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.

Low Temperature Physics•Sep 1, 2007•2 citations

2D Falicov-Kimball Model in the Perturbative Regime at Finite Temperatures

L. Dębski

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.

Acta Physica Polonica A•Jan 1, 2009•1 citation

Thermodynamics of the two-dimensional Falicov-Kimball model: A classical Monte Carlo study

Maciej M. Maśka, Katarzyna Czajka

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.

arXiv:cond-mat/0504533•Physical Review B•Jul 17, 2006•76 citations

Pattern formation in the Falicov–Kimball model

Maciej M. Maśka, Katarzyna Czajka

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)

physica status solidi (b)•Jan 24, 2005•28 citations

Theory and Simulation of the Ising Model

Ashkan Shekaari, Mahmoud Jafari

We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the Hamiltonian of the model have also been presented. We finally have discussed the computational method and details to numerically solve the two- and three-dimensional Ising problems using Monte Carlo simulations. The related computer codes in both Python and Fortran, as well as a simulation trick to visualize the spin lattice, have also been provided.

arXiv:2105.00841•Apr 24, 2021•3 citations
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)
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.
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.
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.
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the Hamiltonian of the model have also been presented. We finally have discussed the computational method and details to numerically solve the two- and three-dimensional Ising problems using Monte Carlo simulations. The related computer codes in both Python and Fortran, as well as a simulation trick to visualize the spin lattice, have also been provided.