2026-09-10T09:44:38Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27759 2026-09-09T12:19:37Z ddc:004 open_access

Glauber Dynamics for Random Field Ising Models on Bounded Degree Graphs Han, Yi Random field Ising model Glauber dynamics Poincaré inequality Markov chain mixing bounded degree graphs We study the ferromagnetic random field Ising model (RFIM) on a graph G = (V,E) having maximal degree Δ, where the external field at each vertex is an i.i.d. random variable. When the random field distribution is sufficiently anti-concentrated, we prove that with high probability over the quenched randomness of the external field, the Glauber dynamics of this RFIM mixes in polynomial time as a consequence of a Poincaré inequality. This model is relevant to the Griffiths phase where the correlations decay exponentially fast in expectation over the quenched random field, but contraction does not hold point-wise due to the existence of weak fields that lead to low-temperature behavior. Previously, fast mixing of Glauber dynamics under large disorder was only proven on the integer lattice, and for RFIM on general graphs, only a sampling algorithm based on self-avoiding walks was known. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yi Han 2026 Is Part Of LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2026.42 urn:nbn:de:0030-drops-277590 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.42 eng https://creativecommons.org/licenses/by/4.0/legalcode