Editing Cluster algorithms
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
'''Cluster algorithms''' are mainly used in the simulation of [[Ising Models|Ising-like models]] | '''Cluster algorithms''' are mainly used in the simulation of [[Ising Models|Ising-like models]]. The essential feature is the use of collective motions of particles (spins) in a single [[Monte Carlo]] step. | ||
An interesting property of some of these | An interesting property of some of these application is the fact that the [[percolation analysis]] of the clusters can | ||
be used to study [[phase transitions]]. | be used to study [[phase transitions]]. | ||
== Swendsen-Wang algorithm == | == Swendsen-Wang algorithm == | ||
Line 30: | Line 30: | ||
the probability of bonding neighbouring sites with equal spins is not set ''a priori'' (See | the probability of bonding neighbouring sites with equal spins is not set ''a priori'' (See | ||
<ref>[http://dx.doi.org/10.1103/PhysRevLett.75.2792 J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, and L. V. Chayes, "Invaded Cluster Algorithm for Equilibrium Critical Points", Physical Review Letters '''75''' pp. 2792-2795 (1995)]</ref>). | <ref>[http://dx.doi.org/10.1103/PhysRevLett.75.2792 J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, and L. V. Chayes, "Invaded Cluster Algorithm for Equilibrium Critical Points", Physical Review Letters '''75''' pp. 2792-2795 (1995)]</ref>). | ||
The algorithm for an Ising system with [[periodic boundary conditions]] can be implemented as follows: | The algorithm for an Ising system with [[boundary conditions |periodic boundary conditions]] can be implemented as follows: | ||
Given a certain configuration of the system: | Given a certain configuration of the system: | ||
Line 81: | Line 81: | ||
== Geometric cluster algorithms == | == Geometric cluster algorithms == | ||
These methods have been proposed for the efficient simulation of continuum fluids, and have been applied to the | |||
simulation of mixtures.<ref>[http://dx.doi.org/10.1103/PhysRevLett.92.035504 Jiwen Liu and Erik Luijten, "Rejection-Free Geometric Cluster Algorithm for Complex Fluids", Physical Review Letters '''92''' 035504 (2004)]</ref> <ref> [http://dx.doi.org/10.1103/PhysRevE.71.066701 Jiwen Liu and Erik Luijten, "Generalized geometric cluster algorithm for fluid simulation", Physical Review E '''71''' 066701 (2005)]</ref> | |||
<ref> [http://dx.doi.org/10.1063/1.1831274 Arnaud Buhot, "Cluster algorithm for nonadditive hard-core mixtures", Journal of Chemical Physics '''122''' 024105 (2005)] </ref> | |||
== Other applications of cluster algorithms == | == Other applications of cluster algorithms == | ||
The cluster algorithms described so far are rejection-free methods, | The cluster algorithms described so far are rejection-free methods, this means that every | ||
new configuration generated | new configuration generated in the sampling is accepted. | ||
rejection-free algorithms. Nevertheless, in | When the complexity of models increases, it becomes difficult to develop efficient | ||
rejection-free algorithms. Nevertheless, in these cases it is still sometimes possible to build up quite efficient cluster algorithms. | |||
Examples: | Examples: | ||
* | *Monte Carlo simulation of atomistic systems with multiparticle moves.<ref>[http://dx.doi.org/10.1063/1.2759924 N. G. Almarza and E. Lomba "Cluster algorithm to perform parallel Monte Carlo simulation of atomistic systems", Journal of Chemical Physics '''127''' 084116 (2007)]</ref>. | ||
== References == | == References == |