Dynamic connectivity algorithms for Monte Carlo simulations of the random-cluster model

We review Sweeny's algorithm for Monte Carlo simulations of the random cluster model. Straightforward implementations suer from the problem of computational critical slowing down, where the computational eort per edge operation scales with a power of the system size. By using a tailored dynamic connectivity algorithm we are able to perform all operations with a poly-logarithmic computational eort. This approach is shown to be ecient in keeping online connectivity information and is of use for a number of applications also beyond cluster-update simulations, for instance in monitoring droplet shape transitions. As the handling of the relevant data structures is non-trivial, we provide a Python module with a full implementation for future reference.