Histogram reweighting

Since many of the histogram-based methods we will outline in the following sections make use of the density of states, the reader may wish to review the material in Chap. 1 regarding its correct treatment in continuum systems. That chapter provides a brief discussion of the subtleties involved, although the reader who is already comfortable with the physical significance behind the density of states may wish to proceed directly. 

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Recently, Orkoulas and Panagiotopoulos [161] have shown that it is possible to use histogram reweighting and multicanonical simulations, starting with individual simulations near the critical point, to map out the liquid-vapour coexistence curve in a very efficient way. 

Ferrenberg A M, Landau D P and Swendsen R H 1995 Statistical errors in histogram reweighting Phys. Rev. E 51 5092-100... 

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

Panagiotopoulos, A. Z. Wong, V. Floriano, M. A., Phase equilibria of lattice polymers from histogram reweighting Monte Carlo simulations, Macromolecules 1998, 31, 912-918... 

In summary, the Gibbs ensemble MC methodology provides a direct and efficient route to the phase coexistence properties of fluids, for calculations of moderate accuracy. The method has become a standard tool for the simulation community, as evidenced by the large number of applications using the method. Histogram reweighting techniques (Chap. 3) have the potential for higher accuracy, especially if... 

The histogram reweighting methodology for multicomponent systems [52-54] closely follows the one-component version described above. The probability distribution function for observing Ni particles of component 1 and No particles of component 2 with configurational energy in the vicinity of E for a GCMC simulation at imposed chemical potentials /. i and //,2, respectively, at inverse temperature ft in a box of volume V is... 

Fig. 10.12. Vapor-liquid phase behavior for the Lennard-Jones fluid. Solid triangles and hollow squares indicate the results of the particle addition/deletion and volume scaling variants of the flat-histogram simulation using the Wang-Landau algorithm. Crosses are from a histogram reweighting study based on grand-canonical measurements at seven state points. The solid line is from Lotfi, et al. [76], Reprinted figure with permission from [75]. 2002 by the American Physical Society...

A more robust (though computationally more intensive) alternative to GDI is provided by a synthesis of extended (multicanonical) sampling and histogram reweighting techniques. The method is bootstrapped by an ES measurement of the full canonical distribution of a suitable order parameter, at some point on the coexistence curve [identified by the equal areas criterion specified in Eq. (10)]. 

The coil-to-globule transition was studied for designed HP copolymer chains both by means of lattice Monte Carlo simulations using bond fluctuation algorithms and multiple histogram reweighting [100,101] and by a numer-... 

For obtaining the canonical distributions, the multiple-histogram reweighting techniques [9,10] are particularly suitable. Suppose we have made a single... 

Fig. 4.2. Time series of potential energy of the C-peptide system from the multi-canonical MD production run (a) and the average potential energy as a function of temperature (b). The latter was obtained from the trajectory of the multicanonical MD production run by the single-histogram reweighting techniques...

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