Monte Carlo method multicanonical

Bhattacharya, K.K. Sethna, J.P., Multicanonical methods, molecular dynamics, and Monte Carlo methods comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562... 

Higo, J. Nakajima, N. Shirai, H. Kidera, A. Nakamura, H., Two-component multicanonical Monte Carlo method for effective conformation sampling, J. Comput. Chem. 1997,18, 2086-2092... 

Figure 8.7 Phase diagram of the conformation of a polymer chain, deduced from theoretical calculations (multicanonical Monte Carlo method Noguchi and Yoshikawa, 1998).

Fig. 3.7. Schematic comparison of the multicanonical and iterative transition-matrix methods. The light gray box indicates a single iteration of several thousand or more individual Monte Carlo steps. The acceptance criterion includes the configuration-space density of the original ensemble, p, and is presented for symmetric moves such as single-particle displacements...

Among the methods discussed in this book, FEP is the most commonly used to carry out alchemical transformations described in Sect. 2.8 of Chap. 2. Probability distribution and TI methods, in conjunction with MD, are favored if there is an order parameter in the system, defined as a dynamical variable. Among these methods, ABF, derived in Chap. 4, appears to be nearly optimal. Its accuracy, however, has not been tested critically for systems that relax slowly along the degrees of freedom perpendicular to the order parameter. Adaptive histogram approaches, primarily used in Monte Carlo simulations - e.g., multicanonical, WL and, in particular, the transition matrix method - yield superior results in applications to phase transitions,... 

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