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- ItemExponential decay of transverse correlations for spin systems with continuous symmetry and non-zero external field(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Lees, Benjamin; Taggi, LorenzoWe 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.