Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 8: Networks: From Topology to Dynamics (joint session DY/SOE)

DY 8.3: Vortrag

Montag, 1. April 2019, 15:30–15:45, H20

Asymptotically Exact Solution of the Fredrickson-Andersen ModelKoray Önder1,2, •Till Kranz1,2, and Matthias Sperl2,11Institut für Theoretische Physik, Uni Köln — 2Institut für Materialphysik im Weltraum, DLR Köln

Kinetically constrained models describe many phenomena from opinion dynamics to amorphous solids [1]. The Fredrickson-Andersen model—a kinetically constrained lattice model—displays an ergodic to non-ergodic transition. Simulations indicate a slow two-step relaxation of dynamical correlation functions close to the transition point. We derive an asymptotically exact solution for the dynamical occupation correlation function of the Fredrickson-Andersen model on the Bethe lattice by identifying an exact expression for its memory kernel. The exact solution proves an empirical scaling relation [2] between critical exponents and allows to calculate the exponents explicitly. In addition, we propose an approximate dynamics that describes numerical data away from the critical point over many decades in time.
[1] F. Ritort and P. Sollich, Adv. Phys. 52, 219 (2003)

[2] M. Sellitto, Phys. Rev. Lett. 115, 225701 (2015)

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