Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 180, Issue 3-4, Pages 1099-1133Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-021-01053-5
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The study demonstrates the exponential decay of transverse correlations in the Spin O(N) model for all N > 1, with a novel result when N > 3. It serves as an alternative to the Lee-Yang theorem for N = 2, 3 and extends to a wide class of multi-component spin systems with continuous symmetry.
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.
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