Damage spreading in the random cluster model

Abstract

We investigate the damage spreading effect in the Fortuin-Kasteleyn random cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D the damage function has a global maximum at p=q/(1+q) for all q>0 and also local maxima at p=1/2 and p=q/(1+q) for q≲0.75. For 3D we observe a local maximum at p=q/(1+q) for q≲0.46 and a global maximum at p=1/2 for q≲4.5. The chaotic phase of the model's (p,q)-parameter space is where the coupling time is of exponential order and we locate points on its boundary. For 3-dimensional grids the lower bound of this phase may be equal to the corresponding critical point of the q-state Potts model for q≥3.