Site-monotonicity properties for reflection positive measures with applications to quantum spin systems

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2713
dc.contributor.authorLees, Benjamin
dc.contributor.authorTaggi, Lorenzo
dc.date.accessioned2022-06-30T12:54:13Z
dc.date.available2022-06-30T12:54:13Z
dc.date.issued2020
dc.description.abstractWe consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application of such a general theorem, we derive site-monotonicity properties for the spin-spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that such spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates -- improving previous positivity results which hold for the Cesàro sum -- and we derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model, lattice permutations, thus extending the previous results of Lees and Taggi (2019).eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9363
dc.identifier.urihttps://doi.org/10.34657/8401
dc.language.isoeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
dc.relation.doihttps://doi.org/10.20347/WIAS.PREPRINT.2713
dc.relation.issn2198-5855
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subjectQuantum spin systemseng
dc.subjectrandom loop modelseng
dc.subjectinfrared boundeng
dc.subjectphase transitionseng
dc.subject.ddc510
dc.titleSite-monotonicity properties for reflection positive measures with applications to quantum spin systemseng
dc.typereporteng
dc.typeTexteng
dcterms.extent13 S.
tib.accessRightsopenAccess
wgl.contributorWIAS
wgl.subjectMathematik
wgl.typeReport / Forschungsbericht / Arbeitspapier
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
wias_preprints_2713.pdf
Size:
255.67 KB
Format:
Adobe Portable Document Format
Description: