论文标题
在随机群集模型中扩散损坏
Damage spreading in the random cluster model
论文作者
论文摘要
我们研究了具有周期性边界的2-维网格的fortuin-kasteleyn随机群集模型中的损伤扩散效果。对于2D，损坏功能在$ p = \ sqrt {q}/（1+\ sqrt {q}）$中的全局最大值，全部$ q> 0 $，以及$ p = 1/2 $和$ p = 1/2 $和$ p = q/（1+q）的本地最大值。对于3D，我们观察到$ p = q/（1+q）的本地最大值，$ q \ lyssim 0.46 $，全球最大值为$ p = 1/2 $，for $ q \ lyssim 4.5 $。模型$（P，Q）$ - 参数空间的混乱阶段是耦合时间的指数顺序，我们在其边界上定位点。对于3维网格，此阶段的下限可能等于$ Q $ Q $ Q \ ge 3 $的$ q $ - 状态POTTS模型的相应临界点。
We investigate the damage spreading effect in the Fortuin-Kasteleyn random cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D the damage function has a global maximum at $p=\sqrt{q}/(1+\sqrt{q})$ for all $q>0$ and also local maxima at $p=1/2$ and $p=q/(1+q)$ for $q\lesssim 0.75$. For 3D we observe a local maximum at $p=q/(1+q)$ for $q\lesssim 0.46$ and a global maximum at $p=1/2$ for $q\lesssim 4.5$. The chaotic phase of the model's $(p,q)$-parameter space is where the coupling time is of exponential order and we locate points on its boundary. For 3-dimensional grids the lower bound of this phase may be equal to the corresponding critical point of the $q$-state Potts model for $q\ge 3$.
