Uniform spanning-tree limit of the random-cluster model
= Uniform spanning-tree limit of the random-cluster model
If $p,q\downarrow0$ with $q/p\to0$, the random-cluster model on a finite connected graph converges to the <uniform spanning tree>. Relative to a tree, an acyclic configuration with $k>1$ components pays a factor $(q/p)^{k-1}$, while every additional cycle pays a factor asymptotic to $p$.