Computer simulations in condensed matter systems: from by Mauro Ferrario, Giovanni Ciccotti, Kurt Binder

By Mauro Ferrario, Giovanni Ciccotti, Kurt Binder

This large and accomplished choice of lectures via world-leading specialists within the box introduces and experiences all correct machine simulation equipment and their functions in condensed topic platforms. quantity 1 is an in-depth advent to an enormous spectrum of computational options for statistical mechanical structures of condensed subject. it is going to allow the graduate scholar and either the professional and nonspecialist researcher to get familiar with the instruments essential to perform numerical simulations at a sophisticated point. quantity 2 released as LNP 704 (ISBN 3-540-35283-X) is a suite of cutting-edge surveys on numerical experiments conducted for a number of platforms, starting from fabrics sciences to chemical biology.

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Because of the hard-core repulsion, a Monte Carlo algorithm involving local moves is relatively inefficient, since any move that generates a particle overlap is rejected. Instead, the geometric cluster algorithm (GCA) [14] is designed to avoid such overlaps while generating a new configuration, by proceeding as follows (cf. Fig. 1). 1. In a given configuration C of particles, a “pivot” is chosen at random. 2. 4 3. The configuration C and its transformed counterpart C˜ are superimposed, which leads to groups of overlapping particles.

41 2 Basic Equipment . . . . . . . . . . . . . . . . . . . . . 2 Statistical Mechanics . . . . . . . . . . . . . . . . . . . . 41 Tools: Elements of Monte Carlo . . . . . . . . . . . . . . . 43 3 Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Meaning and Specification . . . . . . . . . . . . . . . . . . 46 Generic Routes . . . . . .

4 Implementation Issues The actual implementation of the generalized GCA involves a variety of issues. The point reflection with respect to the pivot requires careful consideration of the periodic boundary conditions. Furthermore, as mentioned above, particles that have been translated via a point reflection must not be translated again within the same cluster move, and particles that interact with a given cluster particle both before and after the translation of that cluster particle must be considered only once, on the basis of the difference in pair potential.

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