Ornstein-Zernike Asymptotics for a General "Two-Particle" Lattice Operator

We study the asymptotic behavior of correlations for a general "two-particle" operator T acting on the Hilbert space l(2)(Z(d) x Z(d)), for all dimension d = 1, 2,.... 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 (T-t f((1)), f((2))), t = 1, 2,..., 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.