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Mixing times for the Swapping Algorithm on the Blume‐Emery‐Griffiths model
Author(s) -
Ebbers Mirko,
Knöpfel Holger,
Löwe Matthias,
Vermet Franck
Publication year - 2014
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20461
Subject(s) - mixing (physics) , phase transition , order (exchange) , conjecture , statistical physics , algorithm , struct , mathematics , mean field theory , computer science , discrete mathematics , physics , thermodynamics , condensed matter physics , quantum mechanics , finance , economics , programming language
We analyze the so called Swapping Algorithm, a parallel version of the well‐known Metropolis‐Hastings algorithm, on the mean‐field version of the Blume‐Emery‐Griffiths model in statistical mechanics. This model has two parameters and depending on their choice, the model exhibits either a first, or a second order phase transition. In agreement with a conjecture by Bhatnagar and Randall we find that the Swapping Algorithm mixes rapidly in presence of a second order phase transition, while becoming slow when the phase transition is first order. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 38–77, 2014