Abstract
We discuss the rejection-free event-chain Monte-Carlo algorithm and several applications to dense soft matter systems. Event-chain Monte-Carlo is an alternative to standard local Markov-chain Monte-Carlo schemes, which are based on detailed balance, for example the well-known Metropolis-Hastings algorithm. Event-chain Monte-Carlo is a Markov chain Monte-Carlo scheme that uses so-called lifting moves to achieve global balance without rejections (maximal global balance). It has been originally developed for hard sphere systems but is applicable to many soft matter systems and particularly suited for dense soft matter systems with hard core interactions, where it gives significant performance gains compared to a local Monte-Carlo simulation. The algorithm can be generalized to deal with soft interactions and with three-particle interactions, as they naturally arise, for example, in bead-spring models of polymers with bending rigidity. We present results for polymer melts, where the event-chain algorithm can be used for an efficient initialization. We then move on to large systems of semiflexible polymers that form bundles by attractive interactions and can serve as model systems for actin filaments in the cytoskeleton. The event chain algorithm shows that these systems form networks of bundles which coarsen similar to a foam. Finally, we present results on liquid crystal systems, where the event-chain algorithm can equilibrate large systems containing additional colloidal disks very efficiently, which reveals the parallel chaining of disks.
Highlights
Reviewed by: Nikos Karayiannis, Polytechnic University of Madrid, Spain Georgios Vogiatzis, National Technical University of Athens, Greece
Event-chain Monte-Carlo is a Markov chain Monte-Carlo scheme that uses so-called lifting moves to achieve global balance without rejections. It has been originally developed for hard sphere systems but is applicable to many soft matter systems and suited for dense soft matter systems with hard core interactions, where it gives significant performance gains compared to a local Monte-Carlo simulation
Rejections are avoided, and the entire rejection probability flow is redirected to a lifting move probability flow, which ensures maximal global balance if all physical configurations are probable, i.e., if the Boltzmann distribution for hard spheres holds: The total physical inflow Jap,hgryesen → b,green to (b,green) equals the rejected physical flow Jbp,hgyresen → coll because it involves moving the same sphere by the same distance dw and because physical states a and b are probable
Summary
Since its first application to a hard disk system [1], Monte-Carlo (MC) simulations have been applied to virtually all types of models in statistical physics, both on-lattice and off-lattice. The Metropolis rule (1) satisfies detailed balance for the Boltzmann distribution πa exp(−Ea) if moves are offered with a symmetric trial probability ptrial(a → b) ptrial(b → a) (which is typically fulfilled trivially for standard local MC moves). We point out that detailed balance (for symmetric trial probabilities) and this maximal acceptance rate for energetically downhill moves determine the Metropolis rule for the Boltzmann distribution uniquely. The Swendsen-Wang [3] and Wolff [4] algorithms are the most important cluster algorithms with enormous performance gains close to criticality, where they reduce the dynamical exponent governing the critical slowing down in comparison to local MC simulations These cluster algorithms still fulfill detailed balance but based on a nontrivial trial probability that derives from the cluster construction rules. We discuss in some detail several applications of the EC algorithm in dense soft matter systems, namely polymer systems, liquid crystal systems as well as mixed systems such as liquid crystal colloids
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