Learn More
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 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,(More)
We consider the d-dimensional massless free field localized by a δ-pinning of strength ε. We study the asymptotics of the variance of the field (when d = 2), and of the decay-rate of its 2-point function (when d ≥ 2), as ε goes to zero, for general Gaussian interactions. Physically speaking, we thus rigorously obtain the critical behavior of the transverse(More)
The probabilistic study of effective interface models has been quite active in recent years, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localiza-tion/delocalization transitions. I review some of the results that have been obtained. In particular, I discuss pinning by a local potential,(More)
We consider a model of a two-dimensional interface of the SOS type, with finite-range, even, strictly convex, twice continuously differentiable interactions. We prove that, under an arbitrarily weak potential favouring zero-height, the surface has finite mean square heights. We consider the cases of both square well and δ potentials. These results extend(More)
We show that a class of spin models, containing the Ashkin{Teller model, admits a generalized random{cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison inequalities, still hold for this generalized random{cluster model. Some elementary consequences are given. We also(More)