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  • residual entropy  (2)
  • 2005-2009
  • 1995-1999  (2)
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 93 (1998), S. 33-78 
    ISSN: 1572-9613
    Schlagwort(e): Random external field ; Ising model ; Gibbs states ; ground states ; Bethe lattice ; residual entropy ; dipole configurations ; Griffiths singularities
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The ferromagnetic Ising model on the Bethe lattice of degree k is considered in the presence of a dichotomous external random field ξ x = ±α and the temperature T≥0. We give a description of a part of the phase diagram of this model in the T−α plane, where we are able to construct limiting Gibbs states and ground states. By comparison with the model with a constant external field we show that for all realizations ξ = {ξ x = ±α} of the external random field: (i) the Gibbs state is unique for T 〉 T c (k ≥ 2 and any α) or for α 〉 3 (k = 2 and any T); (ii) the ±-phases coexist in the domain {T 〈 T c, α ≤ H F(T)}, where T c is the critical temperature and H F(T) is the critical external field in the ferromagnetic Ising model on the Bethe lattice with a constant external field. Then we prove that for almost all ξ: (iii) the ±-phases coexist in a larger domain {T 〈 T c, α ≤H F(T) + ε(T)}, where ε(T)〉0; and (iv) the Gibbs state is unique for 3≥α≥2 at any T. We show that the residual entropy at T = 0 is positive for 3≥α≥2, and we give a constructive description of ground states, by so-called dipole configurations.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 84 (1996), S. 1077-1093 
    ISSN: 1572-9613
    Schlagwort(e): Gibbs states ; ground states ; residual entropy ; random field ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibb state is unique for any realization of the external field. Then we prove that asT→0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the external field. The ground state turns out to be a probability measure concentrated on an infinite set of configurations, and we give a constructive description of this measure.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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