Monday, 6 July, 2015

## Published in:

arXiv:1507.01356

The critical surface for random-cluster model with cluster-weight q≥4 on isoradial graphs is identified using parafermionic observables. Correlations are also shown to decay exponentially fast in the subcritical regime. While this result is restricted to random-cluster models with q≥4, it extends the recent theorem of the two first authors to a large class of planar graphs. In particular, the anisotropic random-cluster model on the square lattice is shown to be critical if p_{v}p_{h} / (1−p_{v})(1−p_{h}) = q, where p_{v} and p_{h} denote the horizontal and vertical edge-weights respectively. We also mention consequences for Potts models.