Parallel Multicanonical Simulations and their Application

Generalized-ensemble simulations are advanced Monte Carlo tools to solve problems involving large free-energy barriers and strongly suppressed states, such as first-order phase transitions or rare-event distributions. A particular approach is the multicanonical method, replacing the canonical Boltzmann weight by an auxiliary weight function. The 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. Consequently, 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 $\mathcal{O}(10^5)$ threads. In addition, we present some recent applications using parallel multicanonical simulations to study cluster formation in particle and polymer systems, reaching previously inaccessible scaling regimes.