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  • 1
    Book
    Book
    Berlin [u.a.] : Springer
    Keywords: Lieb, Elliott H. ; Mathematische Physik ; Materie ; Stabilität ; Thomas-Fermi-Modell ; Quantenelektrodynamik ; Bose-Gas ; Functional analysis ; Mathematical physics ; Matter Properties ; Thomas-Fermi theory ; Aufsatzsammlung ; Bibliografie ; Materie ; Stabilität ; Thomas-Fermi-Modell ; Lieb, Elliott H. ; Quantenelektrodynamik ; Bose-Gas
    Type of Medium: Book
    Pages: XV, 932 S. , Ill.
    Edition: 4. ed.
    ISBN: 354022212X
    DDC: 530
    RVK:
    Language: German
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  • 2
    Book
    Book
    Berlin : Springer
    Keywords: Lieb, Elliott H. ; Mathematisches Modell ; Kondensierte Materie ; Mathematisches Modell ; Condensed matter ; Condensed matter Mathematical models ; Aufsatzsammlung ; Bibliografie ; Kondensierte Materie ; Mathematisches Modell ; Lieb, Elliott H.
    Type of Medium: Book
    Pages: IX, 675 S. , graph. Darst. , 235 mm x 155 mm
    ISBN: 3540222987
    DDC: 530.4'1'0151
    RVK:
    RVK:
    RVK:
    Language: English
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 16 (1977), S. 453-461 
    ISSN: 1572-9613
    Keywords: Existence of time evolution ; uniqueness ; strong restoring forces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time evolution is also proven under suitable assumptions on the solutions of the equations of motion.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 22 (1980), S. 297-347 
    ISSN: 1572-9613
    Keywords: Phase transitions ; reflection positivity ; chessboard estimates ; contours
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We discuss applications of the abstract scheme of part I of this work, in particular of infrared bounds and chessboard estimates, to proving the existence of phase transitions in lattice systems. Included are antiferromagnets in an external field, hard-core exclusion models, classical and quantum Coulomb lattice gases, and six-vertex models.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 53 (1988), S. 383-415 
    ISSN: 1572-9613
    Keywords: Quantum antiferromagnet ; Néel order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 12 (1975), S. 291-310 
    ISSN: 1572-9613
    Keywords: Thermodynamic limit ; jellium ; charged particles ; uniform background ; neutral system ; free energy density ; quantum mechanics ; equilibrium statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamic limit of the free energy, energy, pressure, and entropy is established for a neutral system of charged particles interacting with a fixed, uniformly charged background (jellium).
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 18 (1978), S. 335-383 
    ISSN: 1572-9613
    Keywords: Phase transitions ; Heisenberg ferromagnet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 20 (1979), S. 679-693 
    ISSN: 1572-9613
    Keywords: Lattice models ; liquid crystals ; phase transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present five lattice models (two two-dimensional and three three-dimensional) of hard-core particles with attractive interactions and prove (using reflection positivity and the Peierls argument) that they have orientational order at low temperatures; the two-dimensional models have no such ordering if the attractive interaction is not present. We cannot prove that these models do not have complete translational order, but their zero-temperature states are such that we are led to conjecture that complete translational order is always absent.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 53 (1988), S. 1019-1030 
    ISSN: 1572-9613
    Keywords: Néel order ; spin-1/2 antiferromagnets ; infrared bounds ; Gaussian domination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to ber times its value in the other two lattice directions. We prove the existence of Néel order for 0.16⩽r⩽1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 63 (1991), S. 811-816 
    ISSN: 1572-9613
    Keywords: Convexity ; concavity ; eigenvalues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is well known thatσ(H), the sum of the negative eigenvalues of a Hermitian matrixH, is a concave and increasing function ofH. In contrast to this, we prove that forA nonsingular Hermitian andP positive definite, the functionP↦σ(AP)=σ(P 1/2 AP 1/2) is convex and decreasing. Several other results of this nature are also proved.
    Type of Medium: Electronic Resource
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