WIAS Preprint No. 2730, (2020)

Exponential decay of transverse correlations for spin systems with continuous symmetry and non-zero external field


  • Lees, Benjamin
  • Taggi, Lorenzo

2010 Mathematics Subject Classification

  • 82B20 60K35 82B26


  • Spin systems, phase transitions, statistical mechanics




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.

Appeared in

  • Probab. Theory Related Fields, 180 (2021), pp. 1099-1133.

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