# In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusExponential Decay in the Loop O(n) Model on the Hexagonal Lattice for n > 1 and x<13+ε(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x<\tfrac {1}{\sqrt {3}}+\varepsilon (n)$$ \end{document}

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Exponential Decay in the Loop O(n)... [We show that the loop O(n) model on the hexagonal lattice exhibits exponential decay of loop sizes whenever n > 1 and x<13+ε(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x<\tfrac {1}{\sqrt {3}}+\varepsilon (n)$$ \end{document}, for some suitable choice of ε(n) > 0.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusExponential Decay in the Loop O(n) Model on the Hexagonal Lattice for n > 1 and x<13+ε(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x<\tfrac {1}{\sqrt {3}}+\varepsilon (n)$$ \end{document}

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.
15 pages

# References (26)

Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
455 –470
DOI
10.1007/978-3-030-60754-8_21
Publisher site
See Chapter on Publisher Site

### Abstract

[We show that the loop O(n) model on the hexagonal lattice exhibits exponential decay of loop sizes whenever n > 1 and x<13+ε(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x<\tfrac {1}{\sqrt {3}}+\varepsilon (n)$$ \end{document}, for some suitable choice of ε(n) > 0.]

Published: Nov 4, 2020

Keywords: Loop models; O ( n ) model; Phase diagram; Lattice models; Statistical mechanics; Ising model; Enhancement percolation