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

Abstract

The behavior of the bulk two-point correlation function $G(\mathbf{r};T|d)$ 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 $r^{-(d+\sigma )}$, with $2<d<4$, $2<\sigma <4$ and $d+\sigma \le 6$. It is shown that $G(\mathbf{r};T|d)$ decays as $r^{-(d-2)}$ for $1\ll r\ll \xi$, exponentially for $\xi \ll r\ll r^{\ast }$, where $r^{\ast }=(\sigma -2)\xi \ln \xi$, and again in a power law as $r^{-(d+\sigma )}$ for $r\gg r^{\ast }$. The analytical form of the leading-order scaling function of $G(\mathbf{r};T|d)$ in any of these regimes is derived.

12 pages, 3 figures, revtex. Two references added To be published in EPJB

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