发表机构
Eindhoven University of Technology; Utrecht University（埃因霍温理工大学; 乌得勒支大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对随机正则图上的铁磁自旋模型（如Ising和Potts），通过推导配分函数二阶矩的指数增长率表示，并结合淬火压力的集中性，给出了淬火压力等于退火压力的二阶矩证明，为相关文献提供了统一且易读的入口。
AI 中文摘要
随机正则图上的铁磁自旋模型，如Ising和Potts模型，已被广泛研究。其极限压力的若干等价变分和递归表示已知，这些表示可用于建立淬火压力与退火压力之间的一致性。我们简要概述这些表示，并强调不同表述之间的联系。随后，我们推导出配分函数二阶矩指数增长率的类似表示，并证明其与退火压力的平方具有相同的阶，误差为次指数级。结合淬火压力的集中性，这一恒等式在随机正则图上给出了一个清晰的二阶矩证明，证明了淬火与退火的一致性。通过将这些表示和论证统一呈现，我们旨在为随机正则图上铁磁自旋模型的文献提供一个易于理解的入门点。
英文摘要
Ferromagnetic spin models on random regular graphs, such as the Ising and Potts models, have been studied extensively. Several equivalent variational and recursive representations of their limiting pressure are known, and these representations can be used to establish agreement between the quenched and annealed pressures. We give a concise overview of these representations and highlight the connections among the different formulations. We then derive analogous representations for the exponential growth rate of the second moment of the partition function, and prove that it has the same order as the square of the annealed pressure, up to a subexponential error. Combined with concentration of the quenched pressure, this identity yields a transparent second-moment proof of quenched--annealed agreement on random regular graphs. By bringing these representations and arguments together in a unified presentation, we aim to provide an accessible entry point to the literature on ferromagnetic spin models on random regular graphs.
