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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 7: Networks: From Topology to Dynamics I (joint session SOE/DY)
SOE 7.2: Vortrag
Dienstag, 28. März 2023, 11:15–11:30, ZEU 260
Order-disorder transition in the zero-temperature Ising model on random graphs — Armin Pournaki1,2, Eckehard Olbrich2, Sven Banisch3, and •Konstantin Klemm4 — 1Laboratoire Lattice, CNRS & ENS-PSL, Paris — 2Max Planck Institute for Mathematics in the Sciences, Leipzig — 3Karlsruhe Institute for Technology — 4IFISC (UIB-CSIC), Palma de Mallorca, Spain
The zero-temperature Ising model is known to reach a fully ordered ground state in sufficiently dense graphs. In sparse random graphs, the dynamics gets absorbed in disordered local minima at magnetization close to zero. Here we find that the non-equilibrium transition between the ordered and the disordered regime occurs at an average degree that slowly grows with the system size. The system shows bistability: the distribution of the absolute magnetization in the absorbing state reached is bimodal with peaks only at zero and unity. For fixed system size, the average time to absorption behaves non-monotonically as a function of average degree. The peak value of the average absorption time grows as a power law of system size. These findings have relevance for community detection, opinion dynamics and games on networks. Full manuscript available at https://arxiv.org/abs/2209.09325