# Bibliography

Journal Article

### Entropy-driven phase transition in low-temperature antiferromagnetic Potts models

, ,

**: **Communications in Mathematical Physics vol.330, 3 (2014), p. 1339-1394

**: **GA201/09/1931, GA ČR,
GAP201/12/2613, GA ČR

**: **Antiferromagnetic Potts model,
proper coloring,
plane quadrangulation,
phase transition,
diced lattice

**: **http://library.utia.cas.cz/separaty/2014/SI/swart-0429507.pdf

**(eng): **We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.

**: **BA