发表机构
University of California at San Diego; Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加利福尼亚大学圣地亚哥分校; 加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究空间马尔可夫系统中马尔可夫长度发散现象，发现RG无关微扰可产生截止抑制的代数衰减CMI，构造可解模型并预测Toom元胞自动机临界点存在该行为，推导一维CMI衰减与马尔可夫性的等价关系。
AI 中文摘要
条件互信息（CMI）探测空间非马尔可夫性，在近期基于局域可逆性定义混合态相的框架中发挥核心作用。该框架明确区分指数衰减与代数衰减的CMI，因为后者会阻碍其与具有有限马尔可夫长度的态等价。本文证明，流向同一重整化群（RG）不动点的态仍可呈现性质不同的CMI。从有限范围局域经典哈密顿量的临界吉布斯态出发，其CMI在相互作用范围外消失，本文证明，破坏细致平衡的RG无关微扰会普遍产生代数衰减的CMI。关键在于，这些幂律尾受截止抑制：尽管它们在每个有限晶格截止处导致无限马尔可夫长度，但在连续极限中会以截止的正幂次消失。本文构造了展示该现象的可解模型，并预测Toom元胞自动机的伊辛对称临界点普遍表现出此类行为。此外，本文在长程伊辛顺磁体的高温顺磁相中发现了类似的截止抑制CMI，与同一模型中经受连续极限的有限温度临界点处的真实幂律CMI形成对比。本文还推导了一个一般性结果：在一维空间中，当且仅当长程物理是马尔可夫的时，CMI的衰减速度快于缓冲长度的平方倒数。
英文摘要
Conditional mutual information (CMI) probes spatial non-Markovianity and plays a central role in a recently developed framework for defining mixed-state phases based on local reversibility. This framework sharply distinguishes exponentially decaying from algebraically decaying CMI, since the latter obstructs equivalence to a state with finite Markov length. Here we show that states that flow to the same renormalization-group (RG) fixed point can nevertheless exhibit qualitatively different CMI. Starting from a critical Gibbs state of a finite-range local classical Hamiltonian, whose CMI vanishes beyond the interaction range, we show that an RG-irrelevant perturbation that breaks detailed balance generically generates algebraically decaying CMI. Crucially, these power-law tails are cutoff-suppressed: although they lead to an infinite Markov length at every fixed lattice cutoff, they vanish as a positive power of the cutoff in the continuum limit. We construct solvable models that exhibit this phenomenon and predict that the Ising-symmetric critical point of Toom's cellular automata generically exhibits such behavior. We also find analogous cutoff-suppressed CMI in the high-temperature paramagnetic phase of the long-range Ising paramagnet, in contrast with the genuine power-law CMI at the finite-temperature critical point in this same model that survives the continuum limit. We also derive a general result that in one spatial dimension, CMI decays faster than the inverse square of the buffer length if and only if the long-distance physics is Markovian.
Comments5 pages + appendices
