发表机构
Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析活性标量场理论打破细致平衡的两种方式，通过FRG计算得到三维守恒Wilson-Fisher不动点的稳定性矩阵本征值，推导近简并模式的有限尺寸标度，发现电流主导时交叉尺度远超可及系统尺寸。
AI 中文摘要
活性标量场理论在两种物理上截然不同的方式下打破细致平衡：一是通过依赖场的噪声迁移率比Θ(φ)=D(φ)/M(φ)，二是通过Active Model B+的梯度活性。我们对三维空间中守恒Wilson-Fisher不动点受到的此类扰动进行分类。基于Martin-Siggia-Rose-Janssen-De Dominicis（MSRJD）作用量，泛函重整化群（FRG）计算表明，输运部门具有块三角稳定性矩阵，其主导奇模的y_{Θ₁}=-Δ_φ；将梯度部门除以其保持细致平衡的正切后，会留下化学类模式和电流类模式。采用两种光滑调节器得到y_{Θ₁}≈-0.52、y_J≈-0.56、y_{ch}≈-0.89。平移Ward恒等式通过化学梯度模的应力张量散度表示电流算符；守恒性和因果性使活性稳定性矩阵在任意圈阶下均为三角矩阵，且在d=4-ε下的显式两圈计算未发现额外接触抵消项。两个最慢模式仅相差伊辛反常维度，即y_J - y_{Θ₁}=-η。该关系是量纲计数，只要两个算符均未获得额外接触反常（我们在当前截断中为O_Θ建立此条件，并对O_J验证至两圈），则该关系成立；在此条件下，三维参考伊辛值给出y_{Θ₁}≈-0.5181、y_J≈-0.5544。我们推导了这种近简并的宇称分辨有限尺寸标度，识别出可区分两种模式的块可观测量，并表明当电流振幅主导时，交叉尺度远超出任何可及系统尺寸。
英文摘要
We identify the slowest-decaying nonequilibrium perturbations near the three-dimensional conserved Ising critical point and determine their impact on finite-size observables. We study two classes of perturbations: a field-dependent noise-to-mobility ratio $Θ(ϕ)=D(ϕ)/M(ϕ)$ and the gradient activity of Active Model B+. Starting from the Martin-Siggia-Rose-Janssen-De Dominicis action, we compute the linearized flow using the functional renormalization group. The transport sector is block triangular, with leading odd eigenvalue $y_{Θ_1}=-Δ_ϕ$, where $Δ_ϕ=(d-2+η)/2$. In the gradient sector, removing the detailed-balance direction leaves two genuinely nonequilibrium modes, chemical and current-like. Two smooth regulators give $y_{Θ_1}\simeq-0.52$, $y_J\simeq-0.56$, and $y_{\rm ch}\simeq-0.89$. A translation Ward identity expresses the current operator as the divergence of the stress tensor. Together with conservation and Itô causality, this forbids chemical operators from generating the current mode, making the nonequilibrium stability matrix triangular; an independent two-loop calculation in $d=4-\varepsilon$ finds no additional current contact counterterm. Within the FRG truncation, $y_J-y_{Θ_1}=-η$; beyond it, this relation requires the absence of an additional contact anomaly. Using the 3D Ising value $η=0.0362978(20)$ [Kos et al., 2016] gives $y_{Θ_1}\simeq-0.5181$ and $y_J\simeq-0.5544$. Because these exponents nearly coincide, single-power fits yield amplitude-dependent apparent exponents and crossover lengths may exceed accessible system sizes. We derive the resulting finite-size scaling rules: odd block observables respond linearly to activity, while even observables receive only quadratic corrections.
Comments29 pages, 7 figures
