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abstract:
Consider a mixed site-bond percolation problem in two dimensions. The site variables can assume $q$ colors and are subject to couplings $K$ of the Potts type.
Sites of one of these colors are considered `occupied'. Percolation clusters are constructed by placing bonds between `occupied' sites with probability $p$.
This percolation problem is investigated numerically, by means of transfer-matrix and Monte Carlo methods, for a number of choices of $q$ and $K$. In the disordered Potts phase $K<K_c$, the percolation transitions are obviously in the ordinary percolation universality class.
However, for $K \uparrow K_c$, $q$-dependent crossover phenomena appear. The topology of the phase diagram changes in a qualitative sense at $q=2$. For $q<2$ the Potts critical state appears to enhance percolation, for $q>2$ it appears to suppress it.
Remarkably, for $q=2$ the percolation line coincides with the *only* flow line extending to $K<K_c$ from the critical fixed point associated with Potts clusters.