A new computation of the critical point for the planar random-cluster model with q ≥ 1

We present a new computation of the critical value of the random-cluster model with cluster weight q >= 1 on Z(2). This provides an alternative approach to the result in (Probab. Theory Related Fields 153 (2012) 511-542). We believe that this approach has several advantages. First, most of the proof can easily be extended to other planar graphs with sufficient symmetries. Furthermore, it invokes RSW-type arguments which are not based on self-duality. And finally, it contains a new way of applying sharp threshold results which avoid the use of symmetric events and periodic boundary conditions. Some of the new methods presented in this paper have a larger scope than the planar random-cluster model, and may be useful to investigate sharp threshold phenomena for more general dependent percolation processes in arbitrary dimensions.