Improved mixing bounds for the anti-ferromagnetic Potts model on Z2
Leslie Ann Goldberg, Markus Jalsenius, Russell Martin and Mike Paterson
Abstract: The authors of this paper consider the anti-ferromagnetic Potts model on the the integer
lattice Z2. The model has two parameters:
q, the number of spins, and λ = exp(−β),
where β is `inverse temperature'. It is known that the model
has strong spatial mixing if q > 7, or if q = 7 and
λ = 0 or λ > 1/8, or if q = 6 and λ = 0 or
λ > 1/4. The λ = 0 case corresponds to the model in
which configurations are proper q-colourings of
Z2. It is shown that the system has strong spatial
mixing for q ≥ 6 and any λ. This implies that
Glauber dynamics is rapidly mixing (so there is a fully-polynomial
randomised approximation scheme for the partition function), and
also that there is a unique infinite-volume Gibbs state. It is also
shown that strong spatial mixing occurs for a larger range
of λ than was previously known for q = 3, q = 4
and q = 5.
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