Lee-Yang theorems and the complexity of computing averages

Abstract

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. In case of the Ising model, our approach requires us to prove an extension of the famous Lee-Yang Theorem from the 1950s.

30 pages, 3 figures. This version adds definitions of complexity-theoretic terms

References in corpus (2)

• The computational hardness of counting in two-spin models on d-regular graphs
• Partition function zeros at first-order phase transitions: Pirogov-Sinai theory