论文标题
在不符合平面图上的渗透
Ising Percolation on Nonamenable Planar Graphs
论文作者
论文摘要
我们研究无限，及时的，不合同的，平面，单端的$ g $的ISING模型的无限``$+$''或`$ $ - $''簇。如果I.I.D. 〜Bernoulli网站在$ G $上的关键渗透概率$ P_C^{site} $小于$ \ frac {1} {2} {2} $，我们找到了一个明显的区域，以使ising模型的coupl coupl coupl coupl coupl coupl in Infline Infline Infline Infline Infline Infline $ $ $ $ $+++++++++++' ``$ - $'' - 集群，而伊辛模型的随机群集表示没有无限的1个群集。如果$ p_c^{site}> \ frac {1} {2} $，我们以$ p_c^{site} $表示，在ISING模型的随机群集表示中获得关键概率的下限。
We study infinite ``$+$'' or ``$-$'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph $G$ with finite vertex degree. If the critical percolation probability $p_c^{site}$ for the i.i.d.~Bernoulli site percolation on $G$ is less than $\frac{1}{2}$, we find an explicit region for the coupling constant of the Ising model such that there are infinitely many infinite ``$+$''-clusters and infinitely many infinite ``$-$''-clusters, while the random cluster representation of the Ising model has no infinite 1-clusters. If $p_c^{site}>\frac{1}{2}$, we obtain a lower bound for the critical probability in the random cluster representation of the Ising model in terms of $p_c^{site}$.
