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  • 1
    Electronic Resource
    Electronic Resource
    Corrections to the critical temperature in 2D Ising systems with Kac potentials (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 1131-1138 
    Details
    ISSN: 1572-9613
    Keywords: Kac potential ; Ising model ; critical fluctuations ; Euclidean field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider ad=2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling γ〉0 the Kac parameter, we prove that there existsc *〉0 so that the true inverse critical temperature βcr(γ) 〉 1 +by 2 log γ-1, for anyb〈c * and γ correspondingly small. We also show that if γ→0 andb→c *, suitably, then the correlation functions (normalized and rescaled) converge to those of a non-Gaussian Euclidean field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183705
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Upper Bounds on the Critical Temperature for Kac Potentials (1997)
    Springer
    Journal of statistical physics 88 (1997), S. 537-566 
    Details
    ISSN: 1572-9613
    Keywords: Kac potentials ; critical temperature ; fluctuations ; Euclidean field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider an Ising system in two dimensions with a two body ferromagnetic interaction J γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature βcr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C〉0 so that for any b〈C, βcr(γ)〉 1 + bγ2log γ−1 for all γ sufficiently small. The temperature shift Cγ2log γ−1 is to leading orders equal to the covariance of the magnetization fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:JOSS.0000015163.27899.8f
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    Paper (German National Licenses)
    Fulltext
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