• Media type: E-Book; Report; Text
  • Title: Exponential decay of transverse correlations for spin systems with continuous symmetry and non-zero external field
  • Contributor: Lees, Benjamin [Author]; Taggi, Lorenzo [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2020
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2730
  • Keywords: Spin systems -- phase transitions -- statistical mechanics ; 60K35 ; article ; 82B20 ; 82B26
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  • Description: We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem is available, it is an alternative to Lee-Yang when N = 2, 3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a `colour-switch' lemma, and a sampling procedure which allows us to bound from above the `typical' length of the open paths.