Scientific article
Open access

Ornstein-Zernike theory for finite range Ising models above T c

Published inProbability theory and related fields, vol. 125, no. 3, p. 305-349
Publication date2003

We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈s_0 s_x〉_β in the general context of finite range Ising type models on ℤ^d. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of the high temperature region β<βc. As a byproduct we obtain that for every β<βc, the inverse correlation length ξ_β is an analytic and strictly convex function of direction.

Affiliation Not a UNIGE publication
Citation (ISO format)
CAMPANINO, Massimo, IOFFE, Dmitry, VELENIK, Yvan. Ornstein-Zernike theory for finite range Ising models above T c. In: Probability theory and related fields, 2003, vol. 125, n° 3, p. 305–349. doi: 10.1007/s00440-002-0229-z
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Article (Accepted version)
ISSN of the journal0178-8051

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