Download Computer Simulations in Condensed Matter: Systems: From by Mauro Ferrario (Editor), Giovanni Ciccotti (Editor), Kurt PDF

By Mauro Ferrario (Editor), Giovanni Ciccotti (Editor), Kurt Binder (Editor)

This entire choice of lectures via prime specialists within the box introduces and experiences all suitable desktop simulation tools and their functions in condensed subject platforms. quantity 1 is an in-depth advent to an unlimited spectrum of computational suggestions for statistical mechanical platforms of condensed subject. quantity 2 is a set of state of the art surveys on numerical experiments performed for a number of platforms.

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Extra resources for Computer Simulations in Condensed Matter: Systems: From Materials to Chemical Biology. Volume 1

Example text

Whereas the distribution is a monotonously decreasing function of cluster size at high temperatures, it becomes bimodal at temperatures around 25% above the critical temperature. The bimodal form is indicative of the formation of large clusters. It turns out to be possible to influence the cluster-size distribution by placing the pivot in a biased manner. Rather than first choosing the pivot location, a particle is selected that will become the first member of the cluster. Subsequently, the pivot is placed at random within a cubic box of linear size δ, centered around the position of this particle.

A ddimensional “hypercube” of volume Ld , the correlation length is bounded by the linear system size L. Thus, if the temperature approaches Tc , ξ grows according to (15) until it reaches a maximum value ξmax ∝ L, and for temperatures sufficiently close to the critical temperature, (14) is replaced by τ ∝ Lz . (16) We thus encounter a phenomenon called critical slowing down. If a system becomes larger, the correlation time grows very rapidly and it becomes increasingly difficult to generate statistically independent configurations.

Thus, a probability halfway these two extremes is typically chosen in order to maximize the rate at which the system evolves. 2 Indeed, the assignment of bonds involves specific probabilities, but once the clusters have been formed each of them can be flipped independently without imposing an acceptance criterion that involves the energy change induced by such a collective spin-reversal operation. We note that the absence of an acceptance criterion does not imply that a cluster flip does not entail an energy difference!

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