Parallel tempering Monte Carlo

Predescu, C. Predescu, M. Ciobanu, C.V., On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B 2005,109, 4189-4196... 

Yan, Q.L. de Pablo, J.J., Hyper-parallel tempering Monte Carlo Application to the Lennard-Jones fluid and the restricted primitive model, J. Chem. Phys. 1999, 111, 9509-9516... 

Qiliang Yan and Juan J. DePablo, Hyper-Parallel Tempering Monte Carlo and Its Applications Pablo G. Debenedetti, Frank H. Stillinger, Thomas M. Truskett, and Catherine P. Lewis, Theory of Supercooled Liquids and Glasses Energy Landscape and Statistical Geometry Perspectives... 

Atomistic Monte Carlo Simulation of cis-1,4 Polyisoprene Melts. II. Parallel Tempering End-Bridging Monte Carlo Simulations. 

Qiliang Yan and Juan J. DePablo, Hyper-Parallel Tempering Monte Carlo and Its Applications... 

In summary, a promising new method, REPSWA, has been compared and contrasted to existing techniques. Due to its mathematical structure, REPSWA scales linear with system size and has been shown to perform well in model problems. It can easily be combined with parallel tempering and Hybrid Monte Carlo methods to form interesting and exciting novel sampling schemes. These will be described in future work. 

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... 

The feedback-optimized parallel tempering technique [26] outlined in the previous section has recently been applied to study the folding of the 36-residue chicken villin headpiece sub-domain HP-36 [27]. Since HP-36 is one of the smallest proteins with well-defined secondary and tertiary structure [28] and at the same time with 596 atoms still accessible to numerical simulations, it has recently attracted considerable interest as an example to test novel numerical techniques, including molecular dynamics [29,30] and Monte Carlo [31,32] methods. The experimentally determined structure [28] which is deposited in the Protein Data Bank (PDB code Ivii) is illustrated in the left panel of Fig. 6. 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

We have used parallel tempering methods to study the general case of asymmetric primitive models. We use approximately 10 to 15 replicas in our calculations, and the composite system is simulated in parallel for at least 2 X 10 Monte Carlo steps to calculate a coexistence curve. Each Monte Carlo step consists of 200 particle displacements and 100 insertion or deletion attempts. Configuration swaps are attempted every 20 Monte Carlo steps. To estimate critical properties, four or five boxes are simulated in parallel for at least 10 x 10 Monte Carlo steps. Longer simulations are required as the asymmetry of the ions increases. 

Fig. 2. Schematic of the Monte Carlo library design and redesign strategy (from Falcioni and Deem, 2000). (a) One Monte Carlo round with 10 samples an initial set of samples, modification of the samples, measurement of the new figures of merit, and the Metropolis criterion for acceptance or rejection of the new samples, (b) One parallel tempering round with five samples at and five samples at f>2- In parallel tempering, several Monte Carlo simulations are performed at different temperatures, with the additional possibility of sample exchange between the simulations at different temperatures.

The multiple-round, Monte Carlo protocols appear to be especially effective on the more difficult systems with larger numbers of composition and noncomposition variables. That is, the Monte Carlo methods have a tremendous advantage over one-pass methods, especially as the number of variables increases, with parallel tempering the best method. The Monte Carlo... 

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