%0 Generic %1 lees2020exponential %A Lees, Benjamin %A Taggi, Lorenzo %D 2020 %K XY model %T Exponential decay of transverse correlations for O(N) spin systems and related models %U http://arxiv.org/abs/2006.06654 %X 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.

@misc{lees2020exponential, abstract = {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.}, added-at = {2021-12-05T01:29:21.000+0100}, author = {Lees, Benjamin and Taggi, Lorenzo}, biburl = {https://www.bibsonomy.org/bibtex/2173851caf1ed2e41d6d46480bff73f64/gzhou}, description = {Exponential decay of transverse correlations for O(N) spin systems and related models}, interhash = {69c82511f8c4af14a95b49ca701b2818}, intrahash = {173851caf1ed2e41d6d46480bff73f64}, keywords = {XY model}, note = {cite arxiv:2006.06654Comment: 26 pages, 2 Figures. Minor corrections in Lemma 3.1}, timestamp = {2021-12-05T01:29:21.000+0100}, title = {Exponential decay of transverse correlations for O(N) spin systems and related models}, url = {http://arxiv.org/abs/2006.06654}, year = 2020 }