Advanced Studies in Pure Mathematics

Random Path Representation and Sharp Correlations Asymptotics at High-Temperatures

Massimo Campanino, Dmitry Ioffe, and Yvan Velenik

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Abstract

We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of Ornstein-Zernike asymptotics of 2-point functions for self-avoiding walks, Bernoulli percolation and ferromagnetic Ising models. We then extend the proof, in the Ising case, to arbitrary odd-odd correlation functions. We discuss the fluctuations of connection paths (invariance principle), and relate the variance of the limiting process to the geometry of the equidecay profiles. Finally, we explain the relation between these results from Statistical Mechanics and their counterparts in Quantum Field Theory.

Article information

Source
Stochastic Analysis on Large Scale Interacting Systems, T. Funaki and H. Osada, eds. (Tokyo: Mathematical Society of Japan, 2004), 29-52

Dates
Received: 17 January 2003
Revised: 14 April 2003
First available in Project Euclid: 1 January 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546369033

Digital Object Identifier
doi:10.2969/aspm/03910029

Mathematical Reviews number (MathSciNet)
MR2073329

Zentralblatt MATH identifier
1074.82015

Citation

Campanino, Massimo; Ioffe, Dmitry; Velenik, Yvan. Random Path Representation and Sharp Correlations Asymptotics at High-Temperatures. Stochastic Analysis on Large Scale Interacting Systems, 29--52, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/03910029. https://projecteuclid.org/euclid.aspm/1546369033


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