标题： 泛化证明自旋玻璃对称性破缺 显示英文标题

标题： Generic proving of replica symmetry breaking

摘要： 我们通过最近引入的双线性索引（bli）随机过程的插值/比较机制，从一般层面研究了复制对称性破缺（rsb）概念。 特别是， \cite{Stojnicnflgscompyx23}引入了一个\emph{完全提升}（fl）插值机制，\cite{Stojnicsflgscompyx23}开发了其一个\emph{平稳化完全提升}（sfl）变体。 在这里，我们提出一种 sfl\emph{匹配}机制，该机制表明在\cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}中获得的结果与通过统计物理复制工具获得的结果完全对应，该工具的复制对称性破缺（rsb）形式由 Parisi 在\cite{Par79,Parisi80,Par80}中提出。 这些结果非常通用，因为它们可以同时处理几乎所有双线性模型。 此外，鉴于\cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}的结果可以扩展到许多其他形式，这里提出的概念也自动扩展到任何此类形式。 显示英文摘要

摘要： We study the replica symmetry breaking (rsb) concepts on a generic level through the prism of recently introduced interpolating/comparison mechanisms for bilinearly indexed (bli) random processes. In particular, \cite{Stojnicnflgscompyx23} introduced a \emph{fully lifted} (fl) interpolating mechanism and \cite{Stojnicsflgscompyx23} developed its a \emph{stationarized fully lifted} (sfl) variant. Here, we present a sfl \emph{matching} mechanism that shows that the results obtained in \cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23} completely correspond to the ones obtained by a statistical physics replica tool with the replica symmetry breaking (rsb) form suggested by Parisi in \cite{Par79,Parisi80,Par80}. The results are very generic as they allow to handle pretty much all bilinear models at once. Moreover, given that the results of \cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23} are extendable to many other forms, the concepts presented here automatically extend to any such forms as well.