Ornstein-Zernike Asymptotics for a General “Two-Particle” Lattice Operator

We study the asymptotic behavior of correlations for a general “two-particle” operator acting on the Hilbert space , for all dimension d  = 1, 2, . . .. 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...

Full description

Saved in:
Bibliographic Details
Published inCommunications in mathematical physics Vol. 305; no. 3; pp. 605 - 631
Main Authors Boldrighini, C., Minlos, R. A., Pellegrinotti, A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.08.2011
Subjects
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Real Point
Singular Term
Random Walk
Stochastic Operator
Lattice Operator
Online AccessGet full text

Cover

More Information
Summary:We study the asymptotic behavior of correlations for a general “two-particle” operator acting on the Hilbert space , for all dimension d  = 1, 2, . . .. 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 , 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-011-1270-5