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Glauber dynamics Created 2026-09-28 Updated 2026-11-05

Glauber dynamics is a local Markov chain for a spin system. In its heat-bath form, each step chooses one vertex and resamples that spin from its conditional Gibbs distribution given all other spins.

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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 215 / 2 / a / Solution Created 2026-09-28 Updated 2026-10-03

One step of the Glauber dynamics chooses a vertex

v

uniformly and resamples its spin from its conditional Ising model distribution given all other spins. If the proposed new spin is

x

and

S_{v} (σ) = \sum_{w \sim v} σ (w)

, its update probability is

\frac{1}{n} \frac{e ^{β x S_{v} (σ)}}{e ^{β S_{v} (σ)} + e ^{- β S_{v} (σ)}} = \frac{1 + tanh { β x S _{v} ( σ )}}{2 n} .

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