Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point
| Autor: | Yinon Spinka, Alexander Glazman, Hugo Duminil-Copin, Ron Peled |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
60K35
82B20 82B27 Phase transition Applied Mathematics General Mathematics Probability (math.PR) 010102 general mathematics FOS: Physical sciences Observable Mathematical Physics (math-ph) Renormalization group 01 natural sciences Critical point (mathematics) Combinatorics Spin representation Conformal symmetry FOS: Mathematics Hexagonal lattice 0101 mathematics FKG inequality Mathematics - Probability Mathematical Physics Mathematics |
| Zdroj: | Journal of the European Mathematical Society |
| Popis: | The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been predicted by Nienhuis that for $0\le n\le 2$ the loop $O(n)$ model exhibits a phase transition at a critical parameter $x_c(n)=\tfrac{1}{\sqrt{2+\sqrt{2-n}}}$. For $0 Comment: 39 pages, 9 figures; v2 - Theorem 2 now includes uniqueness of the Gibbs measure; v3 - modified statement of Theorem 2, only translation-invariant Gibbs measures are considered, edits in the introduction, to appear in the Journal of the EMS |
| Databáze: | OpenAIRE |
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