论文标题
$ n $ -clock型号：快速和缓慢差异$ n $的变异分析
The $N$-clock model: Variational analysis for fast and slow divergence rates of $N$
论文作者
论文摘要
我们在方格上研究了最近的邻居铁磁自旋系统，其中旋转场被约束以在由$ n $ equi间隔向量（也称为$ n $ clock模型）组成的单位圆的离散化中进行值。对于$ n $ Clock模型的晶格间距，我们发现$ n $的快速发散速率与$ xy $模型的离散到continuum变异限制相同，特别是将能量集中在维度0的拓扑缺陷上。我们证明了$ n $的差异的存在，但要替代$ n $ nivection toctosity是在$ n $ nimodic的存在。 $ bv $ - 总数变化。最后，两种不同类型的极限行为与$ n $的关键制度结合在一起，分析需要辅助笛卡尔电流。
We study a nearest neighbors ferromagnetic spin system on the square lattice in which the spin field is constrained to take values in a discretization of the unit circle consisting of $N$ equi-spaced vectors, also known as $N$-clock model. We find a fast rate of divergence of $N$ with respect to the lattice spacing for which the $N$-clock model has the same discrete-to-continuum variational limit of the $XY$ model, in particular concentrating energy on topological defects of dimension 0. We prove the existence of a slow rate of divergence of $N$ at which the coarse-grain limit does not detect topological defects, but it is instead a $BV$-total variation. Finally, the two different types of limit behaviors are coupled in a critical regime for $N$, whose analysis requires the aid of Cartesian currents.
