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