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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 25 (1972), S. 190-232 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We investigate the general monomer-dimer partition function,P(x), which is a polynomial in the monomer activity,x, with coefficients depending on the dimer activities. Our main result is thatP(x) has its zeros on the imaginary axis when the dimer activities are nonnegative. Therefore, no monomer-dimer system can have a phase transition as a function of monomer density except, possibly, when the monomer density is minimal (i.e.x=0). Elaborating on this theme we prove the existence and analyticity of correlation functions (away fromx=0) in the thermodynamic limit. Among other things we obtain bounds on the compressibility and derive a new variable in which to make an expansion of the free energy that converges down to the minimal monomer density. We also relate the monomer-dimer problem to the Heisenberg and Ising models of a magnet and derive Christoffell-Darboux formulas for the monomer-dimer and Ising model partition functions. This casts the Ising model in a new light and provides an alternative proof of the Lee-Yang circle theorem. We also derive joint complex analyticity domains in the monomer and dimer activities. Our considerations are independent of geometry and hence are valid for any dimensionality.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that Peierls' argument can be extended to prove the coexistence of states which can be transformed into each other only by reflection, inversion or rotation. This makes Peierls' argument applicable to the repulsive lattice gas on a large class of lattices, as well as many models for liquid crystals, ferroelectrics etc. It is specifiquely shown how the argument can be applied to a lattice gas with nearest neighbour repulsion on the hexagonal lattice and the diamond lattice.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die Spin-Bahn-Aufspaltung des X 2 Π-Zustandes von NO wurde mit verschiedenen Potentialen unter Verwendung der SCF LCAO MOs von Brion, Moser und Yamazaki berechnet. Der experimentelle Wert für W (2 Π 3/2) −W (2 Π 1/2) beträgt 122 cm−1. Die Rechnung mittels eines reinen Kernfeldes liefert den Wert 328 cm−1 und unter Einschluß der Abschirmung durch die Elektronen 283 cm−1. Übereinstimmung mit dem experimentellen Wert läßt sich erzielen, wenn man den Exponenten des 2π-Zustandes 30% kleiner als nach den Slater Regeln macht.
    Abstract: Résumé Avec les orbitals moléculaires SCF LCAO de Brion, Moses et Yamazaki, nous avons calculé le dédoublement spin-orbitale de l'état X 2 Π de NO. La valeur expérimentale W (2 Π 3/2) −W (2 Π 1/2) est 122 cm−1. Dans un champ nucléaire «sans écran» on trouve 328 cm−1. L'inclu-sion de l'effet d'écran dû aux répulsions interélectroniques réduit cette valeur à 283 cm−1. La valeur expérimentale s'obtient, si l'on réduit de 30% les exposants d'après Slater dans l'orbi-tale moléculaire 2π.
    Notes: Abstract Using Brion, Moser and Yamazaki's SCF LCAO MO the spin orbit splitting of the X 2 Π state of NO has been calculated using various potentials. Experimentally W (2 Π 3/2) −W (2 Π 1/2) is known to be 122 cm−1. Using an “unscreened” nuclear field we find a value of 328 cm−1. Inclusion of screening due to electronic repulsions reduces this value to 283 cm−1. Agreement with the experimental value may be obtained by reducing the orbital exponents in the 2π molecular orbital by 30% over the value given by Slater's rules.
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Notes: The Hubbard Hamiltonian, while not one of the most successful models for π electrons in benzene, has been extensively investigated in the literature. As part of our general study of that model, we have computed all the energy levels for all values of the repulsion parameter—a task that has not been undertaken before. After extracting all the symmetry of the model we found, to our great surprise, many instances of permanent degeneracy of levels with different symmetry and also crossing of levels of the same symmetry. We can also demonstrate that there is no hidden symmetry to account for these effects. Since these results run counter to one of the oldest folk theorems in quantum chemistry, our otherwise uninspiring graphs may be of general interest.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 20 (1979), S. 371-383 
    ISSN: 1572-9613
    Keywords: Water ; ice ; phase transitions ; lattice gas ; Peierls' argument
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Water-like lattice gases on the triangular and body-centered cubic lattices are investigated. Molecules may reside on the lattice sites in either of two possible orientations, a hydrogen bond being formed between molecules on neighboring sites if they have the proper orientation with respect to one another. For a range of chemical potential at sufficiently low temperatures, the models are shown to have an ordered phase consisting of an open, hydrogen-bonded, icelike structure. The models are shown to be transitionfree at sufficiently high temperature, indicating the existence of a critical point.
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  • 6
    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.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 4 (1972), S. 15-41 
    ISSN: 1572-9613
    Keywords: Polymer ; hydrogen bond ; phase transition ; zeros of partition function ; lattice model ; binary mixture ; ice-rule ferroelectric
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A class of lattice models for a binary mixture is defined by assuming that one of the components may form bonds to neighboring molecules of the same species. It is assumed that the fugacity of a molecule depends on the number of bonds which connect the molecule to other molecules. If no molecule is allowed to be connected by more than two bonds to other molecules, then no phase transition occurs, while phase transition can occur if more than two bonds are allowed. If only two or no bonds are allowed, then the model can be solved rigorously for certain planar lattices by transforming it to a dimer covering problem; this model shows behavior similar to the Ising model in zero magnetic field.
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  • 8
    ISSN: 1572-9613
    Keywords: Lattice gas ; phase transition ; Peierls' argument
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Systems of hard hexagons on a triangular lattice are investigated. The orientation of the hexagons is kept fixed, while the size of the hexagons is varied. The existence of a phase transition is proved for all sizes by means of the Peierls'argument. The proof does not imply a phase transition in the continuous limit.
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