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The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics.
Countable state space Markov random fields and Markov chains on trees
S. Zachary · 1983
Earlier work this paper cites.
Polynomial-time approximation algorithms for the Ising model
M. Jerrum and A. Sinclair · 1993
Earlier work this paper cites.
Hardness of approximating problems on cubic graphs
P. Alimonti and V. Kann · 1997
Earlier work this paper cites.
Fast convergence of the Glauber dynamics for sampling independent sets
M. Luby and E. Vigoda · 1997
Earlier work this paper cites.
On counting independent sets in sparse graphs
M. Dyer, A. Frieze, and M. Jerrum · 1999
Earlier work this paper cites.
Random graphs
S. Janson, T. Łuczak, and A. Rucinski · 2000
Earlier work this paper cites.
On counting independent sets in sparse graphs
M. Dyer, A. Frieze, and M. Jerrum · 2002
Earlier work this paper cites.
Counting independent sets up to the tree threshold
D. Weitz · 2006
Cited alongside, same era.
On the hardness of sampling independent sets beyond the tree threshold
E. Mossel, D. Weitz, and N. Wormald · 2009
Cited alongside, same era.
Gibbs measures and phase transitions on sparse random graphs
A. Dembo and A. Montanari · 2010
Cited alongside, same era.
Ising models on locally tree-like graphs
A. Dembo and A. Montanari · 2010
Cited alongside, same era.
Ising models on power-law random graphs
S. Dommers, C. Giardinà, and R. van der Hofstad · 2010
Cited alongside, same era.
Computational transition at the uniqueness threshold
A. Sly · 2010
Cited alongside, same era.
Factor models on locally tree-like graphs
A. Dembo, A. Montanari, and N. Sun · 2011
Later among the works it cites.
Improved inapproximability results for counting independent sets in the hard-core model
A. Galanis, Q. Ge, D. Štefankovič, E. Vigoda, and L. Yang · 2011
Later among the works it cites.
Correlation decay up to uniqueness in spin systems
L. Li, P. Lu, and Y. Yin · 2011
Later among the works it cites.
Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
A. Sinclair, P. Srivastava, and M. Thurley · 2011
Later among the works it cites.
Inapproximability of the partition function for the antiferromagnetic Ising and hard-core models
A. Galanis, D. Štefankovič, and E. Vigoda · 2012
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The weak limit of Ising models on locally tree-like graphs
A. Montanari, E. Mossel, and A. Sly · 2012
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