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...
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Published in | Communications in mathematical physics Vol. 305; no. 3; pp. 605 - 631 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer-Verlag
01.08.2011
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0010-3616 1432-0916 |
DOI: | 10.1007/s00220-011-1270-5 |