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

Physical review. B, Condensed matter

Thermodynamics of the static approximation in the degenerate Hubbard model

Y. Kakehashi

Published Mar 1, 1985• 9 citations
Publisher

Abstract

The thermodynamics of the static approximation in both the two-field and the vector-field functional integral methods is investigated for the degenerate Hubbard model in the atomic limit. It is shown that the two-field method describes better the thermodynamics of the system; the vector-field method leads to a negative specific heat and unphysical magnetic entropy for temperatures at which the Hund's-rule coupling is dominant.

DOI
10.1103/physrevb.31.3104

Related papers

Critical Study of the Static Functional Integral Method in the Hubbard Model

B. Lorenz, Holger Fehske

Abstract The effect of the static approximation in the functional integral representation of the paramagnetic Hubbard model is critically investigated. The exactly solvable two‐site model is treated within the one‐ and two‐field static functional integral method and some thermodynamic properties (local magnetic moment, specific heat cv) are compared with the exact solution for various interaction strengths and electron densities. It is shown that the static functional integral theory yields unphysical results for cv in the strong interacting system at small densities. The two‐field and one‐field methods are preferable in the low‐ and high‐temperature regions, respectively.

physica status solidi (b)•Nov 1, 1984•0 citations

Static thermodynamic properties of the linear half-filled-band Hubbard model

W. A. Seitz, Daniel Klein

Low-temperature static thermodynamic properties of the linear half-filled-band Hubbard model are computed via a numerical-perturbative method which applies near the atomic limit. Curves for the internal energy, entropy, specific heat, and magnetic susceptibility are reported.

Physical review. B, Solid state•Mar 1, 1974•35 citations

Field and temperature dependence of thermodynamic and correlation functions of Hubbard model

Charles C. Chen, Minghui Huang

The thermodynamic and correlation functions for one- and three- dimensional systems described by the half-filled band Hubbard Hamiltonians are evaluated in the pair-approximation of cluster variation method. The energy, specific heat, magnetization, susceptibility and various equilibrium correlation functions are computed as functions of temperature as well as the external magnetic field for different values of coulomb energies. Our solutions correspond to Bethe approximation in which the relevant pair-correlation functions are included in our formulation. It is observed that the chemical potential for the half-filled band is exactly half of the coulomb energy at all temperatures, irrespective of the value of the applied magnetic field.

Journal of Applied Physics•Mar 1, 1979•5 citations

On the validity of the static approximation in the spin-fluctuation theory for itinerant electrons

Holger Fehske, B. Lorenz

The static approximation in the functional integral theory of itinerant magnetism is critically investigated. For the two-site Hubbard model the local magnetic moment and the specific heat are calculated as functions of temperature and interaction strength. By comparison with the exact results the error in the static approximation is found to be large at low temperatures and for small interaction strengths. It is shown that the subdivision of the ground state into a phase without a local moment (small interaction) and a phase with local moment (large interaction) is induced by the static approximation. The specific heat is underestimated and the zero-point entropy is finite. The implications for the infinite Hubbard model are briefly discussed.

Journal of Physics C Solid State Physics•Oct 10, 1984•2 citations

Thermodynamic properties of a two-dimensional electron gas with attractive interactions

Jorge O. Sofo, C. A. Balseiro

We present a calculation of the thermodynamic properties of a two-dimensional negative-U Hubbard model in the low-density limit. We show that the standard expansion of the thermodynamic potential in terms of particle-particle ladder diagrams evaluated in the undressed fermion propagator, leads to unphysical results like negative entropy and/or specific heat. We propose a phenomenological pair susceptibility that avoids these problems and calculate the entropy and specific heat for different values of the parameters.

Physical review. B, Condensed matter•Apr 1, 1992•19 citations

Thermodynamics of the Planar Hubbard Model

J. Bonča, Peter Prelovšek

The thermodynamic properties: specific heat and entropy are studied as a function of temperature and doping within the two-dimensional Hubbard model with various U/t=4-12. Quantities are calculated using the finite-temperature Lanczos method with additional phase-averaging for a system of 4×4 sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density n~1±0.15 in the whole regime of studied U/t.

International Journal of Modern Physics B•Aug 10, 2003•3 citations
The thermodynamics of the static approximation in both the two-field and the vector-field functional integral methods is investigated for the degenerate Hubbard model in the atomic limit. It is shown that the two-field method describes better the thermodynamics of the system; the vector-field method leads to a negative specific heat and unphysical magnetic entropy for temperatures at which the Hund's-rule coupling is dominant.
Abstract The effect of the static approximation in the functional integral representation of the paramagnetic Hubbard model is critically investigated. The exactly solvable two‐site model is treated within the one‐ and two‐field static functional integral method and some thermodynamic properties (local magnetic moment, specific heat cv) are compared with the exact solution for various interaction strengths and electron densities. It is shown that the static functional integral theory yields unphysical results for cv in the strong interacting system at small densities. The two‐field and one‐field methods are preferable in the low‐ and high‐temperature regions, respectively.
The thermodynamic and correlation functions for one- and three- dimensional systems described by the half-filled band Hubbard Hamiltonians are evaluated in the pair-approximation of cluster variation method. The energy, specific heat, magnetization, susceptibility and various equilibrium correlation functions are computed as functions of temperature as well as the external magnetic field for different values of coulomb energies. Our solutions correspond to Bethe approximation in which the relevant pair-correlation functions are included in our formulation. It is observed that the chemical potential for the half-filled band is exactly half of the coulomb energy at all temperatures, irrespective of the value of the applied magnetic field.
The static approximation in the functional integral theory of itinerant magnetism is critically investigated. For the two-site Hubbard model the local magnetic moment and the specific heat are calculated as functions of temperature and interaction strength. By comparison with the exact results the error in the static approximation is found to be large at low temperatures and for small interaction strengths. It is shown that the subdivision of the ground state into a phase without a local moment (small interaction) and a phase with local moment (large interaction) is induced by the static approximation. The specific heat is underestimated and the zero-point entropy is finite. The implications for the infinite Hubbard model are briefly discussed.
We present a calculation of the thermodynamic properties of a two-dimensional negative-U Hubbard model in the low-density limit. We show that the standard expansion of the thermodynamic potential in terms of particle-particle ladder diagrams evaluated in the undressed fermion propagator, leads to unphysical results like negative entropy and/or specific heat. We propose a phenomenological pair susceptibility that avoids these problems and calculate the entropy and specific heat for different values of the parameters.