AI 中文总结
本文研究Z^d上含Blume-Capel、P(φ)模型的实值自旋模型超临界区域的随机团簇表示，证明其宏观团簇局部唯一性以高概率成立，得到经验磁化强度大偏差的表面阶指数界，填补了非Ising、φ^4模型的相关结果空白。
AI 中文摘要
我们研究了Z^d上一大类实值自旋模型（包括Blume-Capel模型和P(φ)模型）的超临界区域β>β_c，考虑它们的随机团簇表示并证明其表现良好，即宏观团簇的局部唯一性以高概率成立，且在边界条件下均匀一致。这特别意味着经验磁化强度的（下）大偏差满足表面阶指数界，此前这类结果仅在Ising模型和φ^4模型中已知。
英文摘要
We study the supercritical regime $β>β_c$ of a large family of real-valued spin models on $\mathbb Z^d$, including the Blume-Capel and $P(φ)$ models. We consider their random cluster representations and prove that they are well-behaved, in the sense that local uniqueness of macroscopic clusters occurs with high probability, uniformly in the boundary conditions. This implies, among other things, a surface-order exponential bound for the (lower) large deviations of the empirical magnetisation. These results were previously known only in the cases of the Ising and $φ^4$ models.
Comments55 pages, 5 figures
