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  • Finite-size conditions  (1)
  • Quantum systems  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On the Gibbs states for one-dimensional lattice Boson systems with a long-range interaction (1993)
    Springer
    Journal of statistical physics 70 (1993), S. 985-1028 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Quantum systems ; Gibbs states
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider an infinite chain of interacting quantum (anharmonic) oscillators. The pair potential for the oscillators at lattice distanced is proportional to {d 2[log(d+1)]F(d)}−1 where ∑ r∈Z [rF(r)]−1 〈 ∞. We prove that for any value of the inverse temperatureβ〉 0 there exists a limiting Gibbs state which is translationally invariant and ergodic. Furthermore, it is analytic in a natural sense. This shows the absence of phase transitions in the systems under consideration for any value of the thermodynamic parameters.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01053604
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  • 2
    Digitale Medien
    Digitale Medien
    Some remarks on pathologies of renormalization-group transformations for the Ising model (1993)
    Springer
    Journal of statistical physics 72 (1993), S. 1169-1177 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Decimation ; Renormalization-group ; non-Gibbsianness ; Finite-size conditions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The results recently obtained by van Enter, Fernandez, and Sokal on non-Gibbsianness of the measurev =T b μβ,h arising from the application of a single decimation transformationT b , with spacingb, to the Gibbs measure μβ,h , of the Ising model, for suitably chosen large inverse temperatureβ and nonzero external fieldh, are critically analyzed. In particular, we show that if, keeping fixed the same values ofβ, h, andb, one iterates a sufficiently large number of timesn the transformationT b , one obtains a new measurev ′ = (T b )nμβ,h which is Gibbsian and moreover very weakly coupled.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01048184
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