Archive ouverte UNIGE | last documents for author 'Yacine Aoun'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Yacine Aoun'engOrnstein-Zernike behavior for Ising models with infinite-range interactionshttps://archive-ouverte.unige.ch/unige:157675https://archive-ouverte.unige.ch/unige:157675We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work is that the interactions are not assumed to be of finite range. To the best of our knowledge, this is the first proof of OZ asymptotics for a nontrivial model with infinite-range interactions. Our results actually apply to the Green function of a large class of "self-repulsive in average" models, including a natural family of self-repulsive polymer models that contains, in particular, the self-avoiding walk, the Domb-Joyce model and the killed random walk. We aimed at a pedagogical and self-contained presentation.Mon, 03 Jan 2022 11:19:45 +0100Failure of Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small densityhttps://archive-ouverte.unige.ch/unige:151613https://archive-ouverte.unige.ch/unige:151613We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all sufficiently high temperatures and all sufficiently small densities. This turns out to be related to a lack of analyticity of the correlation length as a function of temperature and/or density and even occurs for one-dimensional systems.Wed, 12 May 2021 15:41:15 +0200Non-analyticity of the correlation length in systems with exponentially decaying interactionshttps://archive-ouverte.unige.ch/unige:145018https://archive-ouverte.unige.ch/unige:145018We consider a variety of lattice spin systems (including Ising, Potts and XY models) on Z^d with long-range interactions of the form J_x = psi(x) exp(-|x|), where psi(x) = exp(o(|x|)) and |·| is an arbitrary norm. We characterize explicitly the prefactors psi that give rise to a correlation length that is not analytic in the relevant external parameter(s) (inverse temperature ß, magnetic field h, etc). Our results apply in any dimension. As an interesting particular case, we prove that, in one-dimensional systems, the correlation length is non-analytic whenever psi is summable, in sharp contrast to the well-known analytic behavior of all standard thermodynamic quantities. We also point out that this non-analyticity, when present, also manifests itself in a qualitative change of behavior of the 2-point function. In particular, we relate the lack of analyticity of the correlation length to the failure of the mass gap condition in the Ornstein-Zernike theory of correlations.Mon, 23 Nov 2020 09:32:31 +0100