论文标题
飞机上的模糊potts模型：缩放限制和手臂指数
The fuzzy Potts model in the plane: Scaling limits and arm exponents
论文作者
论文摘要
我们考虑了飞机上的群集重量$ q \ in [1,4）$的关键fortuin-kasteleyn（fk）渗透，并独立于（0,1）$（分别为$ 1-r $）的概率$ r \ in [1,4）$ in [1,4）$ in [1,4）$。我们研究了由此产生的模糊potts模型，该模型与特殊情况下的关键Ising模型相对应，$ q = 2 $和$ r = 1/2 $。我们表明，在假设的假设是，临界FK渗透会收敛到一个不变的缩放限制（已知为FK-asising模型（即$ q = 2 $）收敛，所获得的着色收敛到由Miller，Sheffield和Werner构建和研究的相结合循环集合的变体。基于离散的考虑，我们还表明，离散模型中该着色的ARM指数与连续模型的ARM指数相同。使用连续体中这些手臂指数的值，我们确定模糊potts模型的手臂指数。
We consider a critical Fortuin-Kasteleyn (FK) percolation with cluster weight $q \in [1,4)$ in the plane, and color its clusters in red (respectively blue) with probability $r \in (0,1)$ (respectively $1-r$), independently of each other. We study the resulting fuzzy Potts model, which corresponds to the critical Ising model in the special case $q=2$ and $r=1/2$. We show that under the assumption that the critical FK percolation converges to a conformally invariant scaling limit (which is known to hold for the FK-Ising model, i.e. $q=2$), the obtained coloring converges to variants of Conformal Loop Ensembles constructed, described and studied by Miller, Sheffield and Werner. Based on discrete considerations, we also show that the arm exponents for this coloring in the discrete model are identical to the ones of the continuum model. Using the values of these arm exponents in the continuum, we determine the arm exponents for the fuzzy Potts model.
