Regensburg 2019 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 6: Networks: From Topology to Dynamics (joint session DY/SOE)
SOE 6.3: Vortrag
Montag, 1. April 2019, 15:30–15:45, H20
Asymptotically Exact Solution of the Fredrickson-Andersen Model — Koray Önder1,2, •Till Kranz1,2, and Matthias Sperl2,1 — 1Institut 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)