Cluster Expansions with Renormalized Activities and Applications to Colloids
| Autor: | Dimitrios Tsagkarogiannis, Sabine Jansen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Surface (mathematics)
Nuclear and High Energy Physics 82B05 82D99 Structure (category theory) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Hard spheres Space (mathematics) Grand canonical ensemble 82B05 82D99 Convergence (routing) Cluster (physics) Statistical physics Mathematical Physics Mathematics Cluster expansion |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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