发表机构
University of Illinois Urbana-Champaign; Korea Institute for Advanced Study（伊利诺伊大学厄巴纳-香槟分校; 韩国高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建了含随机矩阵与张量耦合的D维N分量矢量自旋短程模型，证实其大N极限下存在RSB相等，揭示空间局域性约束RSB相的红外机制及帕里西层级的实空间超度量关联特性。
AI 中文摘要
复制对称性破缺（RSB）是平均场自旋玻璃理论的组织原则，但在有限空间维度下，真正的短程系统中是否能出现连续的帕里西（Parisi）层级仍未得到解决。本文介绍了一种在D维超立方格子上的N分量矢量自旋无序模型，其最近邻连键具有随机矩阵耦合，基本 plaquette（ plaquette 指格点的基本面元）具有随机张量耦合。在大N极限下，该模型支持热力学稳定的一步、完全及一步-完全RSB相，同时存在复制对称的顺磁相和铁磁相。我们发现空间局域性通过两种不同的红外机制约束这些有序相：（i）淬火随机各向异性通过Imry-Ma机制在D≤4时破坏均匀铁磁性；（ii）连续帕里西层级产生复制戈德斯通（Goldstone）模式，其无能隙性由沃德（Ward）恒等式保护。在1/N的主导阶下，这些模式表现为自由自旋波带，在D≤2时产生红外发散涨落，以及连续破缺相的Mermin-Wagner不稳定性。值得注意的是，帕里西层级还获得了直接的实空间解释：对于具有相互重叠q的两个纯态，特征长度ξ(q)描述它们的冻结磁化模式差异保持关联的距离。在帕里西层级的连续区间内，ξ(q)与温度无关且随q单调递减。因此，纯态的超度量组织伴随实空间关联长度的超度量层级：在帕里西树根部附近分离的态通过长波长冻结模式产生差异，而离根部更远分离的态仅在逐渐更短的尺度上产生差异。
英文摘要
Replica symmetry breaking (RSB) is the organizing principle of mean-field spin-glass theory, yet whether a continuous Parisi hierarchy can arise in a genuinely short-range system in finite spatial dimension remains unresolved. Here we introduce a disordered model of $N$-component vector spins on a $D$-dimensional hypercubic lattice, with random matrix couplings on nearest-neighbor links and random tensor couplings on elementary plaquettes. In the large-$N$ limit, the model supports thermodynamically stable one-step, full, and one-full RSB phases, alongside replica-symmetric paramagnetic and ferromagnetic phases. We find that spatial locality constrains these ordered phases through two distinct infrared mechanisms. ($i$) Quenched random anisotropy destroys uniform ferromagnetism for $D\leq4$ through an Imry-Ma mechanism. ($ii$) A continuous Parisi hierarchy gives rise to replica Goldstone modes whose gaplessness is protected by a Ward identity. At leading order in $1/N$, these modes behave as a band of free spin waves, producing infrared-divergent fluctuations in $D\leq2$ and a Mermin-Wagner instability of the continuously broken phase. Remarkably, the Parisi hierarchy also acquires a direct real-space interpretation. For two pure states with mutual overlap $q$, a characteristic length $ξ(q)$ describes how far the differences between their frozen magnetization patterns remain correlated. Throughout a continuous sector of the Parisi hierarchy, $ξ(q)$ is independent of temperature and decreases monotonically with $q$. The ultrametric organization of pure states is therefore accompanied by an ultrametric hierarchy of real-space correlation lengths: states that separate near the root of the Parisi tree differ through long-wavelength frozen patterns, whereas states that separate farther from the root differ only on progressively shorter scales.
Comments49 pages, 8 figures
