# Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces (extended abstract)

@inproceedings{Istrail2000StatisticalMT, title={Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces (extended abstract)}, author={Sorin Istrail}, booktitle={STOC '00}, year={2000} }

This work provides an exact characterization, across crystal lattices, of the computational tractability frontier for the partition functions of several Ising models. Our results show that beyond planarity computing partition functions is NP-complete. We provide rigorous solutions to several working conjectures in the statistical mechanics literature, such as the Crossed-Bonds conjecture, and the impossibility to compute effectively the partition functions for any three-dimensional lattice…

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