Ding--Song--Sun不等式：基于最大值原理的证明

中文摘要 AI 辅助

我们证明了在有限铁磁图上的连续自旋模型中，Ding--Song--Sun不等式成立，其中模型的偶数单点势能在其定义域的正半轴上具有凸导数。该类别由Ellis、Monroe和Newman引入，包括$\varphi^4$势和sinh-Gordon势。证明使用了相互作用的秩一插值以及半平面上合作抛物系统的最大值原理。边界条件通过对顶点数和场增量的正坐标数进行归纳得出。特别地，在任意外场中截断的两点函数被其零场值所上界限制。

英文摘要

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.

发表机构

• Weizmann Institute of Science（魏茨曼科学研究所）

机构由 AI 辅助整理，请以论文原文为准。