Cluster expansions with renormalized activities and applications to colloids
Abstract
We consider a binary system of small and large objects in the continuous space interacting via a non-negative potential. By integrating over the small objects, the effective interaction between the large ones becomes multi-body. We prove convergence of the cluster expansion for the grand canonical ensemble of the effective system of large objects. To perform the combinatorial estimate of hypergraphs (due to the multi-body origin of the interaction) we exploit the underlying structure of the original binary system. Moreover, we obtain a sufficient condition for convergence which involves the surface of the large objects rather than their volume. This amounts to a significant improvement in comparison to a direct application of the known cluster expansion theorems. Our result is valid for the particular case of hard spheres (colloids) for which we rigorously treat the depletion interaction.
Keywords
Cite
@article{arxiv.1903.01825,
title = {Cluster expansions with renormalized activities and applications to colloids},
author = {Sabine Jansen and Dimitrios Tsagkarogiannis},
journal= {arXiv preprint arXiv:1903.01825},
year = {2020}
}