DROPS

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.42

Glauber Dynamics for Random Field Ising Models on Bounded Degree Graphs

Authors: Yi Han

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract

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.

Cite as

Yi Han. Glauber Dynamics for Random Field Ising Models on Bounded Degree Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{han:LIPIcs.APPROX/RANDOM.2026.42,
  author =	{Han, Yi},
  title =	{{Glauber Dynamics for Random Field Ising Models on Bounded Degree Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.42},
  URN =		{urn:nbn:de:0030-drops-277590},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.42},
  annote =	{Keywords: Random field Ising model, Glauber dynamics, Poincar\'{e} inequality, Markov chain mixing, bounded degree graphs}
}

Search Results

Documents authored by Han, Yi

Glauber Dynamics for Random Field Ising Models on Bounded Degree Graphs

Abstract

Cite as

Thanks for your feedback!

Could not send message