Improved mixing bounds for the anti-ferromagnetic Potts model on Z^2
| dc.creator | Goldberg, Leslie Ann | |
| dc.creator | Jalsenius, Markus | |
| dc.creator | Martin, Russell | |
| dc.creator | Paterson, Mike | |
| dc.date | 2005-07-27 | |
| dc.date | 2005-11-28 | |
| dc.date.accessioned | 2026-07-07T06:42:18Z | |
| dc.date.available | 2026-07-07T06:42:18Z | |
| dc.description | We consider the anti-ferromagnetic Potts model on the the integer lattice Z^2. The model has two parameters, q, the number of spins, and λ=\exp(-β), where βis ``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 lambda=0 case corresponds to the model in which configurations are proper q-colourings of Z^2. We show 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. We also show that strong spatial mixing occurs for a larger range of λthan was previously known for q = 3, 4 and 5. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0507067 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0507067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101988 | |
| dc.subject | Mathematical Physics | |
| dc.title | Improved mixing bounds for the anti-ferromagnetic Potts model on Z^2 | |
| dc.type | text |