Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs
Publisher
DOI
10.1017/S0963548321000080
Journal
Combinatorics, Probability and Computing
ISSN
0963-5483
Metadata
Show full item recordAbstract
We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding'" technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514–527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.
Authors
Jerrum, M; Dyer, M; Heinrich, M; Müller, HCollections
- Mathematics [1686]