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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.J. Baxter (1982). Exactly Solved Models in Statistical Mechanics, Academic Press, New York.
N.H. Bingham, C.M. Goldie, J.L. Teugels (1987). Regular Variation, Cambridge University Press, Cambridge, U.K.
J. De Coninck (1984). Infinitely divisible distributions functions of class L and the Lee-Yang Theorem, Commun. Math. Phys. 96, 373–385.
R. Cuppens (1975). Decomposition of Multivariate Probabilities, Academic Press, New York.
W. Feller (1971). An Introduction to Probability Theory and its Applications, vol. II, ( 2nd edition ), J. Wiley, New York.
R.B. Griffiths, C.A. Hurst and S. Sherman (1970). Concavity of magnetization of an Ising ferromagnet in a positive external field, J. Math. Phys. 11, 790–798.
Z.J. Jurek (1996). Series of independent exponential random variables. In: Proc 7th Japan-Russia Symposium on Probab. Theory and Math. Statistics, S. Watanabe, M. Fukushima, Yu.V. Prohorov, A.N. Shiryaev, eds., World Scientific, Singapore, pp. 174–182.
Z.J. Jurek (1997). Selfdecomposability: an exception or a rule? Annales Univ. M. Curie-Sklodowska,Lublin-Polonia 51 1,10, Section A, 93–107.
Z.J. Jurek, J.D. Mason (1993). Operator-Limit Distributions in Probability Theory, J. Wiley & Sons, New York.
M.A. Krasnoselskii, Ya. B. Rutickii (1961). Convex Functions and Orlicz Spaces, P. Noordhoff, Groningen.
M. Loeve (1963). Probability Theory, D. van Nostrand Co., Princeton, New Jersey.
Ch. M. Newman (1974). Zeros of the partition function for generalized Ising systems, Commun. Pure and Appl. Math. 27, 143–159.
Ch. M. Newman (1975). Inequalities for Ising models and field theories which obey the Lee-Yang theorem, Commun. Math. Phys. 41, 1–9.
A. Sokal (1981). More inequalities for critical exponents, J. Stat. Phys. 25, 25–50.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1358-1_22
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7111-6
Online ISBN: 978-1-4612-1358-1
eBook Packages: Springer Book Archive