Emergent planarity in two-dimensional Ising models with finite-range Interactions
| Autor: | Hugo Duminil-Copin, Vincent Tassion, Michael Aizenman, Simone Warzel |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Probability (math.PR) 010102 general mathematics FOS: Physical sciences Pfaffian Mathematical Physics (math-ph) 16. Peace & justice Finite range 01 natural sciences Planarity testing Universality (dynamical systems) Theoretical physics Criticality 0103 physical sciences FOS: Mathematics Ising model 010307 mathematical physics 0101 mathematics Stochastic geometry Mathematical Physics Mathematics - Probability Mathematics |
| Zdroj: | Inventiones mathematicae. 216:661-743 |
| ISSN: | 1432-1297 0020-9910 |
| DOI: | 10.1007/s00222-018-00851-4 |
| Popis: | The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on $\mathbb Z^2$ with finite-range interactions. The analysis is enabled by new results on the stochastic geometry of the corresponding random currents. The proven statement establishes an aspect of universality, seen here in the emergence of fermionic structures in two dimensions beyond the solvable cases. Comment: 59 pages, 19 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
| Nepřihlášeným uživatelům se plný text nezobrazuje | K zobrazení výsledku je třeba se přihlásit. |