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

The behavior of the bulk two-point correlation function $G({\bf r};T|d)$ 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 $G({\bf r};T|d)$ decays as $r^{-(d-2)}$ for $1\ll r\ll \xi$, exponentially for $\xi\ll r \ll r^*$, where $r^*=(\sigma-2)\xi \ln \xi$, and again in a power law as $r^{-(d+\sigma)}$ for $r\gg r^*$. The analytical form of the leading-order scaling function of $G({\bf r};T|d)$ in any of these regimes is derived.Comment: 12 pages, 3 figures, revtex. Two references added To be published in EPJ

Fluctuation-induced Interactions in Micro- and Nano-systems: Survey of Some Basic Results

On the examples of the quantum-electrodynamical Casimir force, as well as critical Casimir and Helmholtz forces, we present a review of some results available for the class of fluctuation induced forces. In addition, we also concisely present examples of other such fluctuation-induced forces. On the instance of the Ising model we discuss the connection between the Casimir and Helmholtz forces. We discuss the importance of the presented results for the nanotechnology, and especially for devising micro- or nano-systems, and for their assembly. Some important problems for the nanotechnology, following from the currently available experimental findings, are spelled out and possible strategies for their overcoming are outlined.Comment: 21 pages, 6 figure