Translation-invariant Gibbs states of the Ising model: General setting
| Autor: | Aran Raoufi |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Coupling constant 82B20 010102 general mathematics Regular polygon Invariant (physics) 01 natural sciences amenable graphs percolation 010104 statistics & probability Magnetization Ferromagnetism 60k35 Ising model Gibss states Uniqueness Differentiable function 0101 mathematics Statistics Probability and Uncertainty Mathematics Mathematical physics |
| Zdroj: | Ann. Probab. 48, no. 2 (2020), 760-777 |
| ISSN: | 0091-1798 |
| DOI: | 10.1214/19-aop1374 |
| Popis: | We prove that at any inverse temperature $\beta $ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. The theorem is equivalent with the differentiability of the free energy with respect to the temperature at any temperature. This is obtained for a general class of interactions, that is automorphism-invariant and irreducible coupling constants. The proof uses the random current representation of the Ising model. The result is novel when the graph is not $\mathbb{Z}^{d}$, or when the graph is $\mathbb{Z}^{d}$ but endowed with infinite-range interactions, or even $\mathbb{Z}^{2}$ with finite-range interactions. ¶ Among the other corollaries of this result, we can list continuity of the magnetization at any noncritical temperature and the uniqueness of FK-Ising infinite-volume measures at any temperature. |
| Databáze: | OpenAIRE |
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