Krauth W.'s Introduction to monte-carlo algorithms PDF

By Krauth W.

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All these studies have confirmed our intuition (as long as we stay with purely local Monte Carlo rules): the difference between the two approaches corresponds to a renormalization of time, as soon as go leave a ballistic regime (times large compared to the mean-free time). The Monte Carlo dynamics is very often simpler to study. In equilibrium Monte Carlo, theory does not stop with the naive Metropolis algorithm. Likewise, in dynamical simulation there is also room for much algorithmic subtlety.

A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd edition, Cambridge University Press (1992). [9] E. L. Pollock, D. M. Ceperley Phys. Rev. B 30, 2555 (1984), 36 8343 (1987); D. M. Ceperley Rev. Mod. Phys 67, 1601 (1995) [10] J-S Wang Int. J. Mod. Phys C 5, 707 (1994) [11] W. Krauth, O. Pluchery J. Phys. A: Math Gen 27, L715 (1994) [12] W. Krauth, M. M´ezard Z. Phys. B 97 127 (1995) [13] A. E. Ferdinand and M. E. Fisher Phys. Rev. 185 185 (1969) [14] J. Lee, K. J. Strandburg Phys Rev.

The best general algorithm to actually compute m is of course not “visual inspection of a postscript figure”, but what is called “search of an ordered table”. This you find explained in any book on basic algorithms (cf, for example [8], chap. 2). Locating the correct box only takes of the order of log(N ) operations. The drawback of the computation is therefore that any move costs an order of N operations, since in a sense we have to go through all the possibilities of doing something before knowing our probability “to do nothing”.

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Introduction to monte-carlo algorithms by Krauth W.


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