Kawasaki dynamics beyond the uniqueness threshold Kawasaki dynamics beyond the uniqueness threshold

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random d -regular graph mixes fast beyond the tree uniqueness thres...

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Bibliographic Details
Published in:Probability theory and related fields Vol. 192; no. 1; pp. 267 - 302
Main Authors: Bauerschmidt, Roland, Bodineau, Thierry, Dagallier, Benoit
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2025
Springer Nature B.V
Springer Verlag
Subjects:
Dynamics
Economics
Equilibrium
Ferromagnetism
Finance
Graphs
Insurance
Ising model
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Mathematics and Statistics
Mixtures
Operations Research/Decision Theory
Phase transitions
Polynomials
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistical mechanics
Statistics for Business
Temperature
Theoretical
Uniqueness
39B62 (Functional inequalities
percolation theory
etc.
including subadditivity
60K35 (Interacting random processes; statistical mechanics type models
82B31 (Stochastic methods applied to problems in equilibrium statistical mechanics)
convexity
Random regular graphs
Ising model
Functional inequalities
Conservative dynamics
ISSN:0178-8051, 1432-2064
Online Access:Get full text
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Summary:Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random d -regular graph mixes fast beyond the tree uniqueness threshold when d is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all d ⩾ 3 ). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial.
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content type line 14
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-024-01326-9