Abstract
A class L of Ising models is introduced via Lévy class L characteristic functions. The critical temperature for these new models is associated with the weak law of large numbers, and it is proved that the critical exponent δ is greater than or equal to 1. New inequalities for the Ursell functions are proposed via the Schoenberg Theorem. Moreover, with the functions uo and u1 one associates some Fourier transforms as functions of the external field.
This work, in part, was completed at the Research Center for Molecular Modelling, University of Mons, Mons, Belgium (October 1996— January 1997) with the support of Fondes National de la Recherche Scientifique (FNRS).
The second author was also supported by Grants No. 2 P03 A02914 and A01408 from KBN, Warsaw, Poland.
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De Connick, J., Jurek, Z.J. (2000). Lee-Yang Models, Selfdecomposability and Negative-Definite Functions. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_22
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DOI: https://doi.org/10.1007/978-1-4612-1358-1_22
Publisher Name: Birkhäuser, Boston, MA
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