About: Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

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About: Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1007/s00220-014-2005-1
Description	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. 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. (en)
Title	Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models (en)
skos:prefLabel	Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models (en)
skos:notation	RIV/00216208:11620/14:10285693!RIV15-MSM-11620___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/1931), P(GAP201/12/2613)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Kotecký, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Centrum pro teoretická studia
http://linked.open...dnocenehoVysledku	14737
http://linked.open...ai/riv/idVysledku	RIV/00216208:11620/14:10285693
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	planar graphs; infinite-graphs; random colorings; critical exponents; connective constant; 3 dimensions; zero-temperature; square-lattice; monte-carlo; locally finite graphs (en)
http://linked.open.../riv/klicoveSlovo	3 dimensions connective constant infinite-graphs locally finite graphs random colorings square-lattice zero-temperature planar graphs critical exponents monte-carlo
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[4B6D37099E93]
http://linked.open...i/riv/nazevZdroje	Communications in Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Large interacting lattice systems: Gibbs states and phase transitions Threshold phenomena in stochastic systems
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	330
http://linked.open...iv/tvurceVysledku	Swart, Jan M. Kotecký, Roman Sokal, Alan D.
http://linked.open...ain/vavai/riv/wos	000339156800013
issn	0010-3616
number of pages	56 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00220-014-2005-1
http://localhost/t...ganizacniJednotka	11620

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