PreprintCC BY 4.0arXiv
The Ding--Song--Sun inequality via a maximum principle
Abstract
We prove the Ding--Song--Sun inequality for continuous spin models on finite ferromagnetic graphs whose even single-site potentials have convex derivatives on the positive half of their domain. This class, introduced by Ellis, Monroe and Newman, includes the φ4 and sinh-Gordon potentials. The proof uses a rank-one interpolation of the interactions and a maximum principle for a cooperative parabolic system on a half-plane. The boundary conditions follow by induction on the number of vertices and the number of positive coordinates of the field increment. In particular, the truncated two-point function in an arbitrary external field is bounded above by its zero-field value.
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BibTeX
@misc{ho2026dingsongsun,
title = {{The Ding--Song--Sun inequality via a maximum principle}},
author = {Fu-Hsuan Ho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10528},
eprint = {2609.10528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10528},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Ding--Song--Sun inequality via a maximum principle
AU - Fu-Hsuan Ho
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10528
UR - https://arxiv.org/abs/2609.10528
AB - We prove the Ding--Song--Sun inequality for continuous spin models on finite ferromagnetic graphs whose even single-site potentials have convex derivatives on the positive half of their domain. This class, introduced by Ellis, Monroe and Newman, includes the φ^4 and sinh-Gordon potentials. The proof uses a rank-one interpolation of the interactions and a maximum principle for a cooperative parabolic system on a half-plane. The boundary conditions follow by induction on the number of vertices and the number of positive coordinates of the field increment. In particular, the truncated two-point function in an arbitrary external field is bounded above by its zero-field value.
ER -