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 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 PhysicsMar 1, 19795 citations

Magnetic properties of the hubbard model with strong interaction

V. Ya. Krivnov, Alexander A. Ovchinnikov, Vladyslav O. Cheranovskii

Synthetic MetalsJun 1, 19911 citation

Phase diagram of the simplified Hubbard model with a generalized type of hopping in an external magnetic field

Pavol Farkašovský

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements ${(t}_{\mathrm{ij}}\ensuremath{\sim}{q}^{|i\ensuremath{-}j|})$ the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions $U$ and electron concentrations $n$ . The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements ${(t}_{\mathrm{ij}}\ensuremath{\sim}{q}^{|i\ensuremath{-}j|})$ the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions $U$ and electron concentrations $n$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.

Physical review. B, Condensed matterJun 15, 19986 citations

U

and electron concentrations

n

. The critical value of magnetic field

h

below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.