Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Stochastic Analysis on Large Scale Interacting Systems, T. Funaki and H. Osada, eds. (Tokyo: Mathematical Society of Japan, 2004), 29 - 52
Random Path Representation and Sharp Correlations Asymptotics at High-Temperatures
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.
Received: 17 January 2003
Revised: 14 April 2003
First available in Project Euclid: 1 January 2019
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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