Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs. (12th November 2021)

• Record Type: Journal Article
• Authors: Dyer, Martin; Heinrich, Marc; Jerrum, Mark; Müller, Haiko
• Is Part Of: Combinatorics, probability and computing. Volume 30:Number 6(2021)
• Page Start: 905
• Page End: 921
• Publication Date: 2021-11-12
• Subjects: 68Q25 -- 60J10 -- 68Q17 -- 68W20 -- 68W25 -- 82B20; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548321000080
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract: 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.