Crossing bonds in the random-cluster model.

We derive the scaling dimension associated with crossing bonds in the random-cluster representation of the two-dimensional Potts model by means of a mapping on the Coulomb gas. The scaling field associated with crossing bonds appears to be irrelevant on the critical as well as on the tricritical branch. The latter result stands in a remarkable contrast with the existing result for the tricritical O(n) model that crossing bonds are relevant. Although the O(1) model is equivalent with the q=2 random-cluster model, the crossing-bond exponents obtained for these two models appear to be different. We provide an explanation of this peculiar observation. In order to obtain an independent confirmation of the Coulomb gas result for the crossing-bond exponent, we perform a finite-size-scaling analysis based on numerical transfer-matrix calculations.