Chanal Krauth 2010

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C. Chanal, W. Krauth Convergence and coupling for spin glasses and hard spheres Physical Review E 81 016705 (2010)



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.

Electronic version (arXiv)


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.


Python implementation of the patch algorithm

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