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The Ding-Song-Sun inequality for a class of even ferromagnets
Abstract
Ding-Song-Sun proved the remarkable correlation inequality that the truncated two-point correlation function of ferromagnetic Ising models with arbitrary mixed-sign external field is largest when the field vanishes. This inequality has various important consequences such as log-Sobolev inequalities for Ising and φ4 models up to and at the critical point. We extend the DSS inequality to the class of single spin measures satisfying the GHS condition. This is an important ingredient in our proof of the log-Sobolev inequality for the massless sinh-Gordon model on ℝ2 in a forthcoming article.
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BibTeX
@misc{abdelghani2026dingsongsun,
title = {{The Ding-Song-Sun inequality for a class of even ferromagnets}},
author = {Omar Abdelghani and Roland Bauerschmidt and Thierry Bodineau and Benoit Dagallier},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08980},
eprint = {2609.08980},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08980},
}
RIS
TY - UNPB
TI - The Ding-Song-Sun inequality for a class of even ferromagnets
AU - Omar Abdelghani
AU - Roland Bauerschmidt
AU - Thierry Bodineau
AU - Benoit Dagallier
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.08980
UR - https://arxiv.org/abs/2609.08980
AB - Ding-Song-Sun proved the remarkable correlation inequality that the truncated two-point correlation function of ferromagnetic Ising models with arbitrary mixed-sign external field is largest when the field vanishes. This inequality has various important consequences such as log-Sobolev inequalities for Ising and φ^4 models up to and at the critical point. We extend the DSS inequality to the class of single spin measures satisfying the GHS condition. This is an important ingredient in our proof of the log-Sobolev inequality for the massless sinh-Gordon model on ℝ^2 in a forthcoming article.
ER -