Critical Ising model and spanning trees partition functions
| Autor: | Béatrice de Tilière |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
dimension 2 82B20 [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Mathematics::General Topology FOS: Physical sciences 01 natural sciences Combinatorics dimers 010104 statistics & probability Mathematics::Probability [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Mathematics::Category Theory Mathematics::Metric Geometry Critical Ising model 82B20 82B27 05A19 [MATH]Mathematics [math] 0101 mathematics Mathematical Physics Mathematics Spanning tree 010102 general mathematics Critical two-dimensional Ising model Partition functions Mathematical Physics (math-ph) Statistical mechanics Partition function (mathematics) Graph 05A19 [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Mathematics::Logic Isoradial graphs critical spanning trees Ising model Statistics Probability and Uncertainty 82B27 |
| Zdroj: | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2016, 52 (3), pp.1382-1405 Ann. Inst. H. Poincaré Probab. Statist. 52, no. 3 (2016), 1382-1405 |
| ISSN: | 0246-0203 1778-7017 |
| DOI: | 10.1214/15-aihp680 |
| Popis: | We prove that the squared partition function of the two-dimensional critical Ising model defined on a finite, isoradial graph $G=(V,E)$, is equal to $2^{|V|}$ times the partition function of spanning trees of the graph $\bar{G}$, where $\bar{G}$ is the graph $G$ extended along the boundary; edges of $G$ are assigned Kenyon's [Ken02] critical weights, and boundary edges of $\bar{G}$ have specific weights. The proof is an explicit construction, providing a new relation on the level of configurations between two classical, critical models of statistical mechanics. Comment: 38 pages, 26 figures |
| Databáze: | OpenAIRE |
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