Monte Carlo method replica-exchange

An alternative to these extended ensembles for the simulation of frustrated magnets is the parallel tempering or replica exchange Monte Carlo method [22-25], Instead of performing a single simulation at a fixed temperature, simulations are performed for M replicas at a set of temperatures Ti,T2,. .., Tm- In addition to standard Monte Carlo updates at a fixed temperature, exchange moves are proposed to swap two replicas between adjacent temperatures. These swaps are accepted with a probability... 

Fig. I. Schematic illustration of the implementation of the hyperparallel Monte Carlo method. Each box represents a distinct replica of the simulated system these replicas are simulated simultaneously in a single run. In addition to traditional Monte Carlo trial moves, these replicas can (1) change their state variables in the expanded dimension and (2) exchange configurations with each other, thereby visiting different values of T and fi.

As discussed in Section II. D, the replica exchange Monte Carlo method appears to be an efficient tool for searching the conformational space of reduced protein... 

Replica-exchange Monte Carlo method Parallel tempering... 

In the original implementation of the replica-exchange method (REM) [67-69], Monte Carlo algorithm was used, and only the coordinates q (and the potential energy function E(q)) had to be taken into account. In molecular dynamics algorithm, on the other hand, we also have to deal with the momenta p. We proposed the following momentum assignment in (4.45) (and in (4.46)) [77] ... 

An important exception are atomic simulations of proteins in explicit solvent, where individual particles (e,g, water molecules) represent the solvent Monte Carlo updates of the system would too frequently collide with solvent particles which causes unacceptably high rejection rates of trial moves. In this case, the cooperative many-body motion is more efficiently simulated by integrating the equations of motion of each particle step by step. It can even be most efficient to combine Monte Carlo and nwlecular dynamics. The most prominent hybrid method is replica-exchange molecular dynamics (REMD), where Langevin simulations ran in different threads at various temperatures and the replicas are exchanged after some time steps with the exchange transition probability (4.92), which effectively is a Monte Carlo step. 

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