Archive ouverte UNIGE | last documents for author 'Alexander Glazman'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Alexander Glazman'engProperties of self-avoiding walks and a stress-energy tensor in the O(n) modelhttps://archive-ouverte.unige.ch/unige:87729https://archive-ouverte.unige.ch/unige:87729This thesis is devoted to the study of 2-dimensional models of statistical mechanics. More precisely, we focus on the loop O(n) model and two classical models which can be realized as its particular cases: the Lenz-Ising model (n = 1) and the self-avoiding walk (n = 0). The main goals are to extend our knowledge about these models and to better understand their connection with the Conformal Field Theory which is conjectured to describe the scaling limits. The results known earlier for the self-avoiding walk on the hexagonal lattice are extended to the self-avoiding walk with integrable weights. A discrete stress-energy tensor in the loop O(n) model is constructed and shown to converge to its continuous counterpart for the Ising model. The endpoint of the self-avoiding walk is shown to be delocalized. The main tools used in the thesis are (para)fermionic observable, Yang-Baxter equation and Kesten's pattern lemma.Mon, 26 Sep 2016 09:58:55 +0200On the probability that self-avoiding walk ends at a given pointhttps://archive-ouverte.unige.ch/unige:30543https://archive-ouverte.unige.ch/unige:30543We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x tends to 0 as n tends to infinity, uniformly in x. Also, for any fixed x in Z^d, this probability decreases faster than n^{-1/4 + epsilon} for any epsilon >0. When |x|= 1, we thus obtain a bound on the probability that self-avoiding walk is a polygon.Mon, 21 Oct 2013 11:17:27 +0200