Chanal Krauth 2010
From Werner KRAUTH
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| - | '''C. Chanal, W. Krauth Physical Review E ''' 81''' 016705 (2010)''' | + | '''C. Chanal, W. Krauth '''Convergence and coupling for spin glasses and hard spheres''' Physical Review E ''' 81''' 016705 (2010)''' |
| __FORCETOC__ | __FORCETOC__ | ||
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| [http://arxiv.org/pdf/0910.1530v1 Electronic version (arXiv)] | [http://arxiv.org/pdf/0910.1530v1 Electronic version (arXiv)] | ||
| - | =Comment= | + | =Context= |
| Long version of the [[Chanal Krauth 2008|Chanal Krauth (2008) paper]], containing an extension of the patch algorithm to hard spheres. The connection of the coupling process with damage spreading is made | Long version of the [[Chanal Krauth 2008|Chanal Krauth (2008) paper]], containing an extension of the patch algorithm to hard spheres. The connection of the coupling process with damage spreading is made | ||
| in the [[Bernard Chanal Krauth 2010|2010 paper with Bernard and Chanal]], both for spin glasses and for hard spheres. | in the [[Bernard Chanal Krauth 2010|2010 paper with Bernard and Chanal]], both for spin glasses and for hard spheres. | ||
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| + | =Algorithm= | ||
| [http://www.phys.ens.fr/~krauth/get.php?fichier=pruning_ND.py Python implementation of the patch algorithm] | [http://www.phys.ens.fr/~krauth/get.php?fichier=pruning_ND.py Python implementation of the patch algorithm] | ||
| [[Category:Publication]] [[Category:2010]] [[Category:Algorithm]] [[Category:Hard spheres]] [[Category:Perfect sampling]] | [[Category:Publication]] [[Category:2010]] [[Category:Algorithm]] [[Category:Hard spheres]] [[Category:Perfect sampling]] | ||
Current revision
C. Chanal, W. Krauth Convergence and coupling for spin glasses and hard spheres Physical Review E 81 016705 (2010)
Contents |
Paper
Abstract: We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper bound for the coupling time of a Markov chain for non-trivial statistical-mechanics models. Using the "coupling from the past" protocol, this allows one to exactly sample the underlying equilibrium distribution. For spin glasses in two and three spatial dimensions, the local-patch algorithm works at lower temperatures than previous exact-sampling methods. We discuss variants of the algorithm which might allow one to reach, in three dimensions, the spin-glass transition temperature. The algorithm can be adapted to hard-sphere models. For two-dimensional hard disks, the algorithm allows us to draw exact samples at higher densities than previously possible.
Context
Long version of the Chanal Krauth (2008) paper, containing an extension of the patch algorithm to hard spheres. The connection of the coupling process with damage spreading is made in the 2010 paper with Bernard and Chanal, both for spin glasses and for hard spheres.
