Damage spreading in the random cluster model

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 = root q/(1+ root 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. (c) 2022 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.