标题： 无序系统中的无限稳定性 显示英文标题

标题： Infinite Stability in Disordered Systems

摘要： 在淬火无序系统中，一般认为有序性仅可能存在于弱无序区域（不考虑自旋玻璃类型的模型）。特别是，足够大的随机场预计将禁止任何有限温度下的有序性。在这里，我们证明这未必正确，并且严格地表明对于物理相关系统，在$\mathbb{Z}^d$中具有$d\ge 3$的情况下，无序可以诱导出有序性，这种有序性是\textit{无限稳定}的，即（1）在任意大的无序强度下存在有序状态，（2）在无限无序的极限下，相变温度渐近非零。在二维情况下，如果底层图是非平面的（例如，$\mathbb{Z}^2$点具有最近邻和次近邻相互作用），类似的结果也可以成立。 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 fields is expected to prohibit any finite temperature ordering. Here, we prove that this is not necessarily true, and show rigorously that for physically relevant systems in $\mathbb{Z}^d$ with $d\ge 3$, disorder can induce ordering that is \textit{infinitely stable}, in the sense that (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature is asymptotically nonzero in the limit of infinite disorder. Analogous results can hold in 2 dimensions provided that the underlying graph is non-planar (e.g., $\mathbb{Z}^2$ sites with nearest and next-nearest neighbor interactions).