Lee-Yang theorems and the complexity of computing averages
Computational Complexity
2013-03-07 v2 Statistical Mechanics
Discrete Mathematics
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.
Cite
@article{arxiv.1211.2376,
title = {Lee-Yang theorems and the complexity of computing averages},
author = {Alistair Sinclair and Piyush Srivastava},
journal= {arXiv preprint arXiv:1211.2376},
year = {2013}
}
Comments
30 pages, 3 figures. This version adds definitions of complexity-theoretic terms