Publication Date:
2021-04-28
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 $$N 〉 1$$ N 〉 1 . Our result is new when $$N 〉 3$$ N 〉 3 , in which case no Lee–Yang theorem is available, it is an alternative to Lee–Yang when $$N = 2, 3$$ 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.
Print ISSN:
0178-8051
Electronic ISSN:
1432-2064
Topics:
Mathematics
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