Reweighting methods

Having obtained a set of histograms like Fig. 12 for different system sizes (using histogram reweighting methods [175] in larger systems), the proce-... 

The transitions from the supersaturated vapor to the drop and from the drop to the slab configurations represent barriers in the configuration space which are not removed by the multicanonical reweighting scheme. Hence, these shape transitions limit the applicability of reweighting methods in the study of phase equilibria. 

Fig. 21. Ratio between the interface tension 7 and the simple expression for the strong segregation limit yssL in (54) as a function of inverse incompatibility. Symbols correspond to Monte Carlo results for the bond fluctuation model, the solid line shows the result of the SCF theory, and the dashed line presents first corrections to (54) calculated by Semenov. Also an estimate of the interface tension from the spectrum of capillary waves is shown to agree well with the results of the reweighting method. Adapted from Schmid and Muller [107]...

If this becomes much smaller than the number of points, one must resample and generate some new points. When minimizing the variance, one can also simply neglect the weight factors. Using the reweighting method one can find the optimal value of wavefunction containing tens of parameters. 

Chang, J. Sandler, S.I. Determination of liquid-solid transition using histogram reweighting method and expanded ensemble simulations. J. Chem. Phys. 2003, 118, 8930. 

We have studied the phase and micellization behavior of a series of model surfactant systems using Monte Carlo simulations on cubic lattices of coordination number z = 26. The phase behavior and thermodynamic properties were studied through the use of histogram reweighting methods, and the nanostructure formation was studied through examination ofthe behavior ofthe osmotic pressure as a function of composition and through analysis of configurations. 

We are of the opinion that the tendency of a system to display unilateral or bilateral phase changes is indicative of more serious finite-size effects. Application of the GDI method (or the Gibbs ensemble for that matter) under such circumstances can provide only a qualitative picture of the phase behavior. Histogram-reweighting methods have been developed and refined to the point where they now provide a very precise description of the critical region in the thermodynamic limit. These methods should be applied if a quantitative characterization of the critical region is desired [52-57]. 

Two general observations can be made in relation to this example. First, it should be pointed out that the histogram reweighting method works much faster on smaller system sizes. As the system size inereases, relative... 

A. Ghoufi, F. Goujon, V. Lachet, and P. Malfreyt,/. Chem. Phys., 128, 154716 (2008). Multiple Histogram Reweighting Method for the Surface Tension Calculation. 

Thus, the question is whether the combination of Metropolis data obtained in simulations at different temperatures can yield an improved estimate g E). This is indeed possible by means of the multiple-histogram reweighting method [86], sometimes also called weighted histogram analysis method (WHAM) [87]. Even though the general idea is simple, the actual implementation is not trivial. The reason is that conventional Monte Carlo simulation techniques such as the Metropolis method cannot yield absolute estimates for the partition sum Z T)= g E) i. e., estimates for the density of states at differ-... 

We already know from the optimal arrangement of fragments of the density of states by means of the multi-histogram reweighting method, described in Section 4.5.2, that the optimal error weights are given by the reciprocal variance. Here, we have... 

The efficiency of PERM depends on the simulation temperature. Therefore, a precise estimation of the density of states requires separate simulations at different temperatures. Then, the density of states can be constructed by means of the multiple-histogram reweighting method [86]. Although being a powerful method, it is difficult to keep track of the statistical errors involved in the individual histograms obtained in the simulations. 

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