Exponential decay of transverse correlations for O(N) spin systems and
related models
B. Lees, and L. Taggi. (2020)cite arxiv:2006.06654Comment: 26 pages, 2 Figures. Minor corrections in Lemma 3.1.
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.
Description
Exponential decay of transverse correlations for O(N) spin systems and related models
%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
}