Sweeny dynamics for the random-cluster model with small Q.

The Sweeny algorithm for the Q-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As Q decreases, the so-called critical speeding-up for nonlocal quantities becomes more and more pronounced. However, for some quantity of a specific local pattern, e.

Lifted worm algorithm for the Ising model.

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.

Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions.

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behavior for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.

Fragmentation of fractal random structures.

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions.

Efficient simulation of the random-cluster model.

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation.