Glauber dynamics is a Markov process that updates one spin at a time and preserves a specified Gibbs measure.
In the heat-bath version, each site's rate-one clock replaces its spin by a sample
from the conditional Gibbs measure given all other
spins. For 
sites, its generator is 
, where
is conditional averaging at site 
. The discrete-time version chooses a uniform site at
each attempted update. Its transition matrix
is 
, so 
. Time measured in attempted updates is therefore
times the rate-one-per-site time scale.
For the ferromagnetic Potts model, Blanca et al. (2026) prove mixing in 
times a power of 
individual attempted updates on typical bounded-degree random
regular graphs throughout the tree-uniqueness regime. On
cubes and tori in 
below the corresponding critical inverse temperature, their inverse spectral
gap is 
in discrete single-update time. These bounds use a dichotomy discovered with ChatGPT
assistance.
