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We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs.
Beitrag zur Theorie des Ferromagnetismus
E. Ising · 1925
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Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model
T. D. Lee and C. N. Yang · 1952
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Statistical theory of equations of state and phase transitions. I. Theory of condensation
C. N. Yang and T. D. Lee · 1952
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Lee-Yang theorem and the Griffiths inequality for the anisotropic Heisenberg ferromagnet
T. Asano · 1970
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Zeros of the partition function for the Heisenberg, Ferroelectric, and general Ising models
M. Suzuki and M. E. Fisher · 1971
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On a problem of Spencer
J. B. Shearer · 1985
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Random generation of combinatorial structures from a uniform distribution
M. Jerrum, L. G. Valiant, and V. V. Vazirani · 1986
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Approximating the permanent
M. Jerrum and A. Sinclair · 1989
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Polynomial-time approximation algorithms for the Ising model
M. Jerrum and A. Sinclair · 1993
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Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case
F. Martinelli and E. Olivieri · 1994
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Approach to equilibrium of Glauber dynamics in the one phase region: II. The general case
F. Martinelli and E. Olivieri · 1994
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Griffiths’ singularities in diluted Ising models on the Cayley tree
J. C. A. Barata and D. H. U. Marchetti · 1997
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Approximately counting up to four
M. Luby and E. Vigoda · 1997
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Sampling spin configurations of an Ising system
D. Randall and D. Wilson · 1999
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Enumerative Combinatorics
R. Stanley and S. Fomin · 1999
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On the distribution and gap structure of Lee–Yang zeros for the Ising model: Periodic and aperiodic couplings
J. C. A. Barata and P. S. Goldbaum · 2001
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The computational complexity of two-state spin systems
L. A. Goldberg, M. Jerrum, and M. Paterson · 2003
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Glauber dynamics on trees: Boundary conditions and mixing time
F. Martinelli, A. Sinclair, and D. Weitz · 2004
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The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lovász Local Lemma
A. Scott and A. Sokal · 2004
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Glauber dynamics on trees and hyperbolic graphs
N. Berger, C. Kenyon, E. Mossel, and Y. Peres · 2005
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Counting independent sets up to the tree threshold
D. Weitz · 2006
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The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability
J. Borcea and P. Brändén · 2009
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The Lee-Yang and Pólya-Schur programs. II. Theory of stable polynomials and applications
J. Borcea and P. Brändén · 2009
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Negative dependence and the geometry of polynomials
J. Borcea, P. Brändén, and T. Liggett · 2009
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Graph homomorphisms with complex values: A dichotomy theorem
J.-Y. Cai, X. Chen, and P. Lu · 2010
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Computing the partition function for cliques in a graph
A. Barvinok · 2015
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Computing the permanent of (some) complex matrices
A. Barvinok · 2015
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Interlacing families I: Bipartite Ramanujan graphs of all degrees
A. Marcus, D. Spielman, and N. Srivastava · 2015
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Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem
A. W. Marcus, D. A. Spielman, and N. Srivastava · 2015
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Combinatorics and Complexity of Partition Functions
A. Barvinok · 2016
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Computing the partition function for graph homomorphisms
A. Barvinok and P. Soberón · 2016
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A complexity dichotomy for partition functions with mixed signs
L. A. Goldberg, M. Grohe, M. Jerrum, and M. Thurley · 2010
Cited alongside, same era.
Characterization of Lee-Yang polynomials
D. Ruelle · 2010
Cited alongside, same era.
Approximating partition functions of the two-state spin system
J. Zhang, H. Liang, and F. Bai · 2011
Cited alongside, same era.
Critical Ising on the square lattice mixes in polynomial time
E. Lubetzky and A. Sly · 2012
Cited alongside, same era.
Left and Right Convergence of Graphs with Bounded Degree
C. Borgs, J. Chayes, J. Kahn, and L. Lovász · 2013
Cited alongside, same era.
Correlation decay up to uniqueness in spin systems
L. Li, P. Lu, and Y. Yin · 2013
Cited alongside, same era.
Computing the partition function for graph homomorphisms with multiplicities
A. Barvinok and P. Soberón · 2016
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Benjamini–Schramm continuity of root moments of graph polynomials
P. Csikvári and P. E. Frenkel · 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. Štefankovic, E. Vigoda, and Y. Yin · 2016
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The complexity of approximately counting in 2-spin systems on k k -uniform bounded-degree hypergraphs
A. Galanis and L. A. Goldberg · 2016
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Uniqueness, spatial mixing, and approximation for ferromagnetic 2-spin systems
H. Guo and P. Lu · 2016
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FPTAS for hardcore and Ising models on hypergraphs
P. Lu, K. Yang, and C. Zhang · 2016
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Spatial mixing and the connective constant: Optimal bounds
A. Sinclair, P. Srivastava, D. Štefankovič, and Y. Yin · 2016
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Counting hypergraph matchings up to uniqueness threshold
R. Song, Y. Yin, and J. Zhao · 2016
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A generalization of permanent inequalities and applications in counting and optimization
N. Anari and S. O. Gharan · 2017
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Random cluster dynamics for the Ising model is rapidly mixing
H. Guo and M. Jerrum · 2017
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Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
V. Patel and G. Regts · 2017
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Real stable polynomials and matroids: Optimization and counting
D. Straszak and N. K. Vishnoi · 2017
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