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We define a discrete-time Markov chain for abstract polymer models and show that under sufficient decay of the polymer weights, this chain mixes rapidly.
General properties of polymer systems
C. Gruber and H. Kunz · 1971
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Phase diagrams of classical lattice systems
S. A. Pirogov and Ya. G. Sinai · 1975
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Cluster expansion for abstract polymer models
R. Kotecký and D. Preiss · 1986
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A unified approach to phase diagrams in field theory and statistical mechanics
C. Borgs and J. Z. Imbrie · 1989
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Interfaces in the Potts model I: Pirogov-Sinai theory of the Fortuin-Kasteleyn representation
L. Laanait, A. Messager, S. Miracle-Solé, J. Ruiz, and S. Shlosman · 1991
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Comparison techniques for random walk on finite groups
P. Diaconis and L. Saloff-Coste · 1993
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Comparison theorems for reversible Markov chains
P. Diaconis and L. Saloff-Coste · 1993
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Estimates of semi-invariants for the Ising model at low temperatures
R. L. Dobrushin · 1996
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Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics
C. Borgs, J. T. Chayes, A. Frieze, J. H. Kim, P. Tetali, E. Vigoda, and V. H. Vu · 1999
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On Markov chains for independent sets
M. E. Dyer and C. S. Greenhill · 2000
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Analyzing Glauber dynamics by comparison of Markov chains
D. Randall and P. Tetali · 2000
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Loss network representation of Peierls contours
R. Fernández, P. A. Ferrari, and N. L. Garcia · 2001
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Absence of zeros for the chromatic polynomial on bounded degree graphs
C. Borgs · 2006
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Markov chain comparison
M. E. Dyer, L. A. Goldberg, M. Jerrum, and R. Martin · 2006
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Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphs
D. Galvin and P. Tetali · 2006
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Counting independent sets up to the tree threshold
D. Weitz · 2006
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Approximation algorithms for the normalizing constant of Gibbs distributions
M. Huber · 2015
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FPTAS for #BIS with degree bounds on one side
J. Liu and P. Lu · 2015
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Mixing of the Glauber dynamics for the ferromagnetic Potts model
M. Bordewich, C. Greenhill, and V. Patel · 2016
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Convergence of MCMC and loopy BP in the tree uniqueness region for the hard-core model
C. Efthymiou, T. P. Hayes, D. Štefankovič, E. Vigoda, and Y. Yin · 2016
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Combinatorics and Complexity of Partition Functions
A. Barvinok · 2017
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Deterministic polynomial-time approximation algorithms for functions and graph polynomials
V. Patel and G. Regts · 2017
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Random Walks on Combinatorial Objects
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