Parallel multicanonical simulations applied to equilibrium cluster formation

Cluster formation occurs in supersaturated or supercooled solutions and involves a large free-energy barrier. For equilibrium systems in the canonical ensemble, this free-energy barrier diverges with system size. Such problems that involve large free-energy barriers can be efficiently studied with flat-histogram Monte-Carlo algorithms that artificially enhance the probability of otherwise suppressed states. One particular flat-histogram algorithm is the multicanonical method, where an auxiliary weight function is iteratively adapted to produce a flat histogram. The beauty of this approach is that each iteration samples from an equilibrium distribution due to fixed weights, such that this process can be parallelized very easily and very efficiently. We will present in detail this parallel scheme for CPU and GPU architectures and show its close-to-perfect scaling up to 10k threads. In addition, we present recent applications using parallel multicanonical simulations to study cluster formation in particle and polymer systems, reaching previously inaccessible scaling regimes.