Communications in Mathematical Physics

, Volume 329, Issue 3, pp 827–858

Lee–Yang Theorems and the Complexity of Computing Averages


DOI: 10.1007/s00220-014-2036-7

Cite this article as:
Sinclair, A. & Srivastava, P. Commun. Math. Phys. (2014) 329: 827. doi:10.1007/s00220-014-2036-7


We study the complexity of computing average quantities related to spin systems, such as the mean magnetization and susceptibility in the ferromagnetic Ising model, and the average dimer count (or average size of a matching) in the monomer-dimer model. By establishing connections between the complexity of computing these averages and the location of the complex zeros of the partition function, we show that these averages are #P-hard to compute, and hence, under standard assumptions, computationally intractable. In the case of the Ising model, our approach requires us to prove an extension of the famous Lee–Yang Theorem from the 1950s.

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Soda HallUniversity of California BerkeleyBerkeleyUSA

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