Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs

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 an...

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Bibliographic Details
Published in:Combinatorics, probability & computing Vol. 30; no. 6; pp. 905 - 921
Main Authors: Dyer, Martin, Heinrich, Marc, Jerrum, Mark, Müller, Haiko
Format: Journal Article
Language:English
Published: Cambridge Cambridge University Press 01.11.2021
Subjects:
Algorithms
Antiferromagnetism
Approximation
Combinatorics
Graphs
Ising model
Kagome lattice
Markov chains
Mathematical analysis
Partitions (mathematics)
Polynomials
ISSN:0963-5483, 1469-2163
Online Access:Get full text
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Summary: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.
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ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548321000080