标题： 无限稳定的无序系统在涌现的分形结构上 显示英文标题

标题： Infinitely Stable Disordered Systems on Emergent Fractal Structures

摘要： 在淬火无序系统中，通常认为有序性仅可能存在于弱无序区域（忽略自旋玻璃型模型）。 特别是，足够大的随机场预计会阻止任何有限温度的有序性。 在这里，我们表明这并不总是正确的。 我们提供了物理上合理的例子，说明在这些系统中，无序会引发一种*无限稳定*的有序性，具体而言：(1) 在任意大的无序强度下都存在有序性，(2) 在无序无限大的极限下，相变温度仍会渐近地保持非零。 这种有序性在由无序诱导的、出现的渗透分形结构的边界上是空间局域化的。 我们给出的例子最自然地描述为当空间维度 $d \ge 3$时的情况，但也可以在 $d=2$时进行表述，前提是底层图是非平面的。 显示英文摘要

摘要： In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit any finite temperature ordering. Here, we show that this is not necessarily true. We provide physically motivated examples of systems in which disorder induces an ordering that is *infinitely stable* in the sense that: (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature remains, asymptotically, nonzero in the limit of infinite disorder. The ordering is spatially localized on the boundary of a disorder-induced, emergent percolating fractal structure. The examples we give are most naturally described when the spatial dimension $d \ge 3$, but can also be formulated when $d=2$, provided that the underlying graph is non-planar.