Ornstein-Zernike Asymptotics for a General 'Two-Particle' Lattice Operator
| Autor: | Alessandro Pellegrinotti, Carlo Boldrighini, R. A. Minlos |
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| Přispěvatelé: | C., Boldrighini, R. A., Minlo, Pellegrinotti, Alessandro |
| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Communications in Mathematical Physics. 305:605-631 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-011-1270-5 |
| Popis: | We study the asymptotic behavior of correlations for a general “two-particle” operator $${{\mathcal T}}$$ acting on the Hilbert space $${\ell_2({\mathbb Z}^d\times {\mathbb Z}^d)}$$ , for all dimension d = 1, 2, . . .. $${{\mathcal T}}$$ is written as the sum of a “main” term, and a small “interacting” term, a form which appears in many problems. If the interacting term is small, we give a complete description of the asymptotics for large t of the correlations $${({\mathcal T}^{t} f^{(1)}, f^{(2)}), t=1,2,\ldots}$$ , for f (1), f (2) in some suitable class. The asymptotics is of the Ornstein-Zernike type, i.e., exponential with a power-law factor, which is t −d for d ≥ 3, but for d = 1, 2 it can be “anomalous” and is determined by the interacting term. |
| Databáze: | OpenAIRE |
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