Rigorous nonperturbative Ornstein-Zernike theory for Ising ferromagnets

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 th...

A pr 2 00 3 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 th...

Ornstein-zernike Theory for the Finite Range Ising

Ising Meets Ornstein and Zernike, Debye and Hückel, Widom and Rowlinson, and Others

The name Ising has come to stand not only for a specific model, but for an entire universality class arguably the most important such class in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising universality appears or is pertinent. The “Ornstein-Zernike” connection concerns a thermodynamically self-consistent closure of the eponymous rela...

N ov 2 00 1 ORNSTEIN - ZERNIKE THEORY FOR THE FINITE RANGE ISING MODELS ABOVE

We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈σ0σx〉β in the general context of finite range Ising type models on Z . 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 ...