AI 中文总结
该研究探究不可逆多数阈值动力学的行为，发现其会冻结平衡非一致迷宫，确定粗域布局的确定性机制，揭示冻结壁的挫败特征，丰富了阈值动力学的形态调控认知。
AI 中文摘要
多数阈值动力学中，每个智能体采用加权邻域中的主导状态，将二值场弛豫至一致态或条纹态。我们研究该规则不可逆化后的情况：每个智能体通过晶格上的高斯核相互作用，最多从其局部加权少数态翻转一次。可逆形式是Merriman-Bence-Osher型阈值动力学，为可精确求解的校准模型，其界面以平均曲率运动，具有闭式晶格钉扎和迁移率。不可逆性改变了结果：从随机初始条件出发，单次翻转规则会冻结平衡的非一致迷宫，而可逆弛豫会使这些迷宫消失。该图案化区域是初始自旋组成围绕平衡的窗口，随相互作用范围增大而变窄，由标准化偏置控制，其起始在四倍范围内与尺度无关。冻结形态是 arrested coarsening：在平衡时双连续，特征宽度亚线性增长，大尺度下低于相互作用范围。我们通过干预确定机制：固定初始条件，改变更新顺序，发现粗域布局是确定性的，更新顺序仅在次要的首次通过竞争中起作用，该竞争微调确定性动力学已设定的壁位置。这些壁由挫败标记：智能体违背自身局部场而被冻结。该特征在任何可逆弛豫中均不存在，绝大多数为界面性，几乎不承载图案的大尺度形状。
英文摘要
Majority threshold dynamics, in which each agent adopts the dominant state in a weighted neighborhood, relaxes a binary field toward consensus or stripes. We study what happens when this rule is made irreversible: each agent, interacting through a Gaussian kernel on a lattice, may flip out of its local weighted minority at most once. The reversible form is threshold dynamics of Merriman-Bence-Osher type, an exactly solvable calibration in which interfaces move by mean curvature with closed-form lattice pinning and mobility. Irreversibility changes the outcome. From random initial conditions, the one-flip rule freezes balanced non-consensus labyrinths that reversible relaxation drives away. The patterned regime is a window of initial spin compositions around equal balance, narrowing as the interaction range grows, controlled by a standardized bias whose onset is independent of scale over a fourfold range. The frozen morphology is arrested coarsening: bicontinuous at balance, with a feature width that grows sublinearly and falls below the interaction range at large scales. We determine the mechanism by intervention. Fixing the initial condition while varying the update order shows that the coarse domain layout is deterministic, while the update order enters only in a secondary first-passage race that fine-tunes the wall positions the deterministic dynamics has already set. Those walls are marked by frustration: agents frozen against their own local field. This signature is identically absent from any reversible relaxation, is overwhelmingly interfacial, and carries almost none of the pattern's large-scale shape.
Comments13 pages, 7 figures
