Skip to main content

A Power-Law Upper Bound on the Correlations in the 2D Random Field Ising Model

Author(s): Aizenman, Michael; Peled, Ron

Download
To refer to this page use: http://arks.princeton.edu/ark:/88435/pr16d5pb3r
Full metadata record
DC FieldValueLanguage
dc.contributor.authorAizenman, Michael-
dc.contributor.authorPeled, Ron-
dc.date.accessioned2024-01-23T15:02:41Z-
dc.date.available2024-01-23T15:02:41Z-
dc.date.issued2019-06-06en_US
dc.identifier.issn0010-3616-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr16d5pb3r-
dc.description.abstractAs first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all temperatures, through the addition of quenched random magnetic field of uniform variance, even if that is small. This statement is quantified here by a power-law upper bound on the decay rate of the effect of boundary conditions on the magnetization in finite systems, as function of the distance to the boundary. Unlike exponential decay which is only proven for strong disorder or high temperature, the power-law upper bound is established here for all field strengths and at all temperatures, including zero, for the case of independent Gaussian random field. Our analysis proceeds through a streamlined and quantified version of the Aizenman–Wehr proof of the Imry–Ma rounding effect.en_US
dc.languageenen_US
dc.language.isoen_USen_US
dc.relation.ispartofCommunications in Mathematical Physicsen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleA Power-Law Upper Bound on the Correlations in the 2D Random Field Ising Modelen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s00220-019-03450-3-
dc.identifier.eissn1432-0916-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

Files in This Item:
File Description SizeFormat 
s00220-019-03450-3.pdf496.56 kBAdobe PDFView/Download


Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.