Log In Sign Up

Optimal Mixing Time for the Ising Model in the Uniqueness Regime

by   Xiaoyu Chen, et al.

We prove an optimal O(n log n) mixing time of the Glauber dynamics for the Ising models with edge activity β∈(Δ-2/Δ, Δ/Δ-2). This mixing time bound holds even if the maximum degree Δ is unbounded. We refine the boosting technique developed in [CFYZ21], and prove a new boosting theorem by utilizing the entropic independence defined in [AJK+21]. The theorem relates the modified log-Sobolev (MLS) constant of the Glauber dynamics for a near-critical Ising model to that for an Ising model in a sub-critical regime.


page 1

page 2

page 3

page 4


Optimal mixing for two-state anti-ferromagnetic spin systems

We prove an optimal Ω(n^-1) lower bound for modified log-Sobolev (MLS) c...

Rapid mixing of Glauber dynamics via spectral independence for all degrees

We prove an optimal Ω(n^-1) lower bound on the spectral gap of Glauber d...

A Near-Linear Time Sampler for the Ising Model

We give a near-linear time sampler for the Gibbs distribution of the fer...

The Critical Mean-field Chayes-Machta Dynamics

The random-cluster model is a unifying framework for studying random gra...

A Matrix Trickle-Down Theorem on Simplicial Complexes and Applications to Sampling Colorings

We show that the natural Glauber dynamics mixes rapidly and generates a ...

Entropic Independence II: Optimal Sampling and Concentration via Restricted Modified Log-Sobolev Inequalities

We introduce a framework for obtaining tight mixing times for Markov cha...