Two-point correlation function in systems with van der Waals type interaction

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The behavior of the bulk two-point correlation function G(r;T|d) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r⁻⁽ᵈ⁺σ⁾, with 2<d<4, 2<σ<4 and d+σ≤ 6. It is shown that G(r;T|d) decays as r⁻⁽ᵈ⁻²⁾ for 1≪ r≪ ξ, exponentially for ξ≪ r ≪ r*, where r*=(σ-2)ξ ξ, and again in a power law as r⁻⁽ᵈ⁺σ⁾ for r≫ r*. The analytical form of the leading-order scaling function of G(r;T|d) in any of these regimes is derived.