标题： 一维Potts模型零温度Glauber动力学中的畴尺寸分布 显示英文标题

标题： Distribution of domain sizes in the zero temperature Glauber dynamics of the 1 D Potts model

摘要： 对于零温度Glauber动力学的$q$状态Potts模型，我们通过将其问题映射到一个精确可解的一物种凝聚模型（$A+A\rightarrow A$）来计算域大小的精确分布。在长时间极限下，这个分布是普遍的，并且从其（复杂）精确表达式中，我们提取了其在各种区域中的行为。我们的结果在模拟中进行了测试，并与最近提出的一个简单近似预测进行了比较。考虑域壁的动力学作为反应扩散模型$ A+A \to \ A $，概率为$ (q-2)/(q-1)$，以及概率为$1/(q-1)$的$A+A \to \emptyset $，我们在长时间范围内计算了对相关函数。 显示英文摘要

摘要： For the zero temperature Glauber dynamics of the $q$-state Potts model, we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one-species coagulation model ($A+A\rightarrow A$). In the long time limit, this distribution is universal and from its (complicated) exact expression, we extract its behavior in various regimes. Our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently. Considering the dynamics of domain walls as a reaction diffusion model $ A+A \to \ A $ with probability $ (q-2)/(q-1)$ and $A+A \to \emptyset $ with probability $1/(q-1)$, we calculate the pair correlation function in the long time regime.