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Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics

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7 Author(s)
Borgs, C. ; Microsoft Corp., Redmond, WA, USA ; Chayes, J.T. ; Frieze, A. ; Jeong Han Kim
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Studies two widely used algorithms, Glauber dynamics and the Swendsen-Wang (1987) algorithm, on rectangular subsets of the hypercubic lattice Zd. We prove that, under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in Ld-1. In other words, under these circumstances, the mixing in these widely used algorithms is not rapid; instead it is torpid. The models we study are the independent set model and the q-state Potts model. For both models, we prove that Glauber dynamics is torpid in the region with phase coexistence. For the Potts model, we prove that the Swendsen-Wang mixing is torpid at the phase transition point

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Foundations of Computer Science, 1999. 40th Annual Symposium on

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