0429507 20240103204403.720140819235959.9 000339156800013 84903891784 10.1007/s00220-014-2005-1 56 s. P cav_un_epca*02564310010-36163303 (2014)1339-1394Springer Antiferromagnetic Potts model proper coloring plane quadrangulation phase transition diced lattice cav_un_auth*0291434 Kotecký R. CZ 34 cav_un_auth*0305398 Sokal A.D. US 33 cav_un_auth*0217893 Swart Jan M. Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics 33 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2014/SI/swart-0429507.pdf GA201/09/1931 GA ČR cav_un_auth*0254026 GAP201/12/2613 GA ČR cav_un_auth*0291241 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. 2015 BA 3 4 A 4a 20231122140318.4 RVO:67985556 http://hdl.handle.net/11104/0235499 cav_un_auth*0304565 University of Warwick GB cav_un_auth*0304566 CTS Center for Theoretical Study, Charles University CZ cav_un_auth*0298189 New York University US S PHYSICSMATHEMATICAL 2.007 1.587 Q1 97.834 87.963 Q1* Q1* 2014 Soubory v repozitáři: swart-0429507.pdf 84903891784 SCOPUS 000339156800013 WOS cav_un_epca*0256431 Communications in Mathematical Physics 0010-3616 1432-0916 Roč. 330 č. 3 2014 1339 1394 Springer