Dyer, M orcid.org/0000-0002-2018-0374, Heinrich, M, Jerrum, M et al. (1 more author) (2021) Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs. Combinatorics, Probability and Computing, abs/2005.07944. ISSN 0963-5483
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been published in a revised form in Combinatorics, Probability and Computing [http://doi.org/10.1017/S0963548321000080]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Author(s), 2021. Published by Cambridge University Press |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/S016562/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 May 2021 14:44 |
Last Modified: | 12 Oct 2021 00:38 |
Status: | Published online |
Publisher: | Cambridge University Press (CUP) |
Identification Number: | 10.1017/S0963548321000080 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162602 |