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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 58 (1990), S. 265-293 
    ISSN: 1572-9613
    Keywords: Debye screening ; cluster expansion, stability of matter
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(β, z) denotes the thermodynamic pressure at inverse temperatureβ and activityz, then it follows from the Mayer expansion thatp(β, z) is infinitely differentiable providedβ andβz are sufficiently small. Here it is shown that there existsβ 0〉0 such thatp(β, z) is infinitely differentiable ifβ〈β 0 andz〉0. One can interpret this result as saying that (β 0)−1 is an upper bound on the critical temperature for the system.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 64 (1991), S. 251-270 
    ISSN: 1572-9613
    Keywords: Heisenberg model ; random walk ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We develop random walk representations for the spin-S Heisenberg ferromagnet with nearest neighbor interactions. We show that the spin-S Heisenberg model is a diffusion with local times controlled by the spin-S Ising model. As a consequence, expectations for the Heisenberg model conditioned on zero diffusion are shown to be Ising expectations.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 92 (1998), S. 571-586 
    ISSN: 1572-9613
    Keywords: Numerical simulations ; random walks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper is concerned with the numerical simulation of a random walk in a random environment in dimension d = 2. Consider a nearest neighbor random walk on the 2-dimensional integer lattice. The transition probabilities at each site are assumed to be themselves random variables, but fixed for all time. This is the random environment. Consider a parallel strip of radius R centered on an axis through the origin. Let X R be the probability that the walk that started at the origin exits the strip through one of the boundary lines. Then X R is a random variable, depending on the environment. In dimension d = 1, the variable X R converges in distribution to the Bernoulli variable, X ∞ = 0, 1 with equal probability, as R → ∞. Here the 2-dimensional problem is studied using Gauss-Seidel and multigrid algorithms.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 23 (1991), S. 223-231 
    ISSN: 1573-0530
    Keywords: 82D40 ; 82B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The authors obtain an upper bound on the free energy of the spin 1/2 Heisenberg ferromagnet. The zero field bound is, at low temperature, similar to the formula given by the magnon approximation. That is, its functional dependence on temperature is the same but the constant is different.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of theoretical probability 13 (2000), S. 427-489 
    ISSN: 1572-9230
    Keywords: diffusion process ; elliptic operator ; Lipschitz manifolds ; random walks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d≥2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d−1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d−1 dimensional manifolds which are C 1, α , and also d−1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 65 (1991), S. 235-245 
    ISSN: 1572-9613
    Keywords: Classical Heisenberg model ; free energy ; Gaussian model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that the free energy of the classical Heisenberg model converges to the free energy of the Gaussian in the low-temperature limit. The limit is uniform as the field is taken to zero.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 84 (1996), S. 415-454 
    ISSN: 1572-9613
    Keywords: Directed polymer ; Brownian motion ; transfer matrix ; spectral gap
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 363-374 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract LetH N be the quantum mechanical Hamiltonian for a neutral system of 2N charged particles, each of unit charge. The HamiltonianH N is assumed to act on wave functions ψ inL 2(ℝ6N ) which satisfy Bose statistics. It is shown that if the kinetic energy of ψ is sufficiently small, then 〈ψ|H N |ψ〉≧−CN 7/5 for some universal constantC.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 125 (1989), S. 153-180 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the quantum Coulomb Gas ofN particles with HamiltonianH at low temperature and negative values of the chemical potentialμ. Ifμ is sufficiently negative the Coulomb gas is approximately a perfect rare gas of charged particles, as expected. The interesting fact is that for higher (but still negative) values ofμ the gas changes to a rare gas of some atom or molecule (which is most likely neutral). The type of molecule is determined by the ground state of the HamiltonianH —μN with center of mass motion removed.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 88 (1983), S. 133-150 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Consider a large number of electrons with Coulomb repulsion moving under the influence of static nuclei. It is assumed the potentials due to the nuclei are Coulombic away from their centers but are smooth at the centers, so no singularities exist. The author shows that the exchange energy for the Hartree-Fock ground state of this system converges in a suitable limit to the formula obtained by Dirac for exchange energy as an integral of the one body density.
    Type of Medium: Electronic Resource
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