Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
The Swendsen-Wang process does not always mix rapidly
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Approximating the partition function of the ferromagnetic Potts model
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Exponential time complexity of the permanent and the Tutte polynomial
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The complexity of approximately counting stable matchings
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
The complexity of approximately counting stable matchings
Theoretical Computer Science
The complexity of approximately counting stable roommate assignments
Journal of Computer and System Sciences
Approximating the partition function of the ferromagnetic Potts model
Journal of the ACM (JACM)
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
Journal of Computer and System Sciences
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
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We consider the complexity of approximating the partition function of the ferromagnetic Ising model with varying interaction energies and local external magnetic fields. Jerrum and Sinclair provided a fully polynomial randomized approximation scheme for the case in which the system is consistent in the sense that the local external fields all favour the same spin. We characterize the complexity of the general problem by showing that it is equivalent in complexity to the problem of approximately counting independent sets in bipartite graphs, thus it is complete in a logically defined subclass of #P previously studied by Dyer, Goldberg, Greenhill and Jerrum. By contrast, we show that the corresponding computational task for the $q$-state Potts model with local external magnetic fields and $q2$ is complete for all of #P with respect to approximation-preserving reductions.