SKM 2021 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 5: Poster Session III: Statistical Physics, Complex Fluids and Soft Matter
DY 5.11: Poster
Dienstag, 28. September 2021, 17:30–19:30, P
Ornstein-Zernike relation in hypergraphs — •Christian Faber1,2,3, Till Kranz2,3, and Matthias Sperl3,2 — 1Jülich Supercomputing Centre, FZ Jülich — 2Institut für Theoretische Physik, Uni Köln — 3Institut für Materialphysik im Weltraum, DLR Köln
The pair correlation function is an important input to describe equilibrium phase transitions and the glass transitions [1]. An Ornstein-Zernike relation can be used to represent the pair correlation function in a form that is easy to approximate and that allows an intuitive representation in terms of graphs [2]. However, this graphical representation is limited to pairwise interactions between particles and recent analyses show that some systems, such as foams, cannot be adequately represented with pair interactions [3]. To be able to specify a meaningful Ornstein-Zernike relation for such systems, we have started from scratch and have introduced hypergraphs for multi-body interactions. With these we are able to represent the Ornstein-Zernike relation for multi-body interactions and to give a graphical meaning to the individual terms. We will discuss the similarities and differences between the relation for pair- and for multi-body interactions.
[1] W. Götze, Zeitschrift f. Physik B Condensed Matter 60, 2 (1985).
[2] M. Wortis, "Linked Cluster Expansion" in Phase Transitions and Critical Phenomena, C. Domb, M.S. Green, Eds. (Academic Press, London, 1974), vol. 3.
[3] G. Ginot, R. Höhler, S. Mariot, A. Kraynik, W. Drenckhan, Soft Matter 15.22, 4570-4582 (2019).