标题： 无序系统中长程有序的稳定性：一种广义的丁庄论证 显示英文标题

标题： The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument

摘要： 在淬火无序下长程有序的稳定性是统计力学中的核心问题。 本文开发了一个广义框架，扩展了 Ding-Zhuang 方法，并结合了 Pirogov-Sinai 框架，建立了一个系统方案，用于研究无序系统中长程有序的相变。 我们将 Ding-Zhuang 方法公理化为一个包含 Peierls 条件和局部对称条件的理论框架。 对于满足这些条件的维度$d \geq 3$系统，我们在低温和弱无序下证明了长程有序的持续存在，并存在多个共存的不同 Gibbs 态。 该框架的通用性在多种模型中得到展示，为将 Peierls 方法系统地扩展到无序系统提供了支持。 显示英文摘要

摘要： The stability of long-range order against quenched disorder is a central problem in statistical mechanics. This paper develops a generalized framework extending the Ding-Zhuang method and integrated with the Pirogov-Sinai framework, establishing a systematic scheme for studying phase transitions of long-range order in disordered systems. We axiomatize the Ding-Zhuang approach into a theoretical framework consisting of the Peierls condition and a local symmetry condition. For systems in dimensions $d \geq 3$ satisfying these conditions, we prove the persistence of long-range order at low temperatures and under weak disorder, with multiple coexisting distinct Gibbs states. The framework's versatility is demonstrated for diverse models, providing a systematic extension of Peierls methods to disordered systems.