Published January 2020
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Zeros of ferromagnetic 2-spin systems
- Creators
- Guo, Heng
- Liu, Jingcheng
- Lu, Pinyan
Abstract
We study zeros of the partition functions of ferromagnetic 2-state spin systems in terms of the external field, and obtain new zero-free regions of these systems via a refinement of Asano's and Ruelle's contraction method. The strength of our results is that they do not depend on the maximum degree of the underlying graph. Via Barvinok's method, we also obtain new efficient and deterministic approximate counting algorithms. When the edge interaction is attractive for both spins, our algorithm outperforms all other methods such as Markov chain Monte Carlo and correlation decay.
Additional Information
© 2020 by SIAM. We would like to thank the organisers of the workshop "Deterministic Counting, Probability, and Zeros of Partition Functions" in the Simons Institute for the Theory of Computing. The topic of the workshop inspired us to look at this problem and the work was initiated during the workshop. We thank anonymous reviewers for helpful comments on an early version of the paper. HG wants to thank the hospitality of the Institute of Theoretical Computer Science in Shanghai University of Finance and Economics, where part of the work was done. JL was a PhD student at UC Berkeley when this work was carried out, and was supported by US NSF grant CCF-1815328. PL is supported by NSFC grant 61922052 and 61932002, Innovation Program of Shanghai Municipal Education Commission, Program for Innovative Research Team of Shanghai University of Finance and Economics, and the Fundamental Research Funds for the Central Universities.Attached Files
Published - 1.9781611975994.11.pdf
Submitted - 1907.06156.pdf
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Additional details
- Eprint ID
- 105142
- Resolver ID
- CaltechAUTHORS:20200828-121031001
- CCF-1815328
- NSF
- 61922052
- National Natural Science Foundation of China
- 61932002
- National Natural Science Foundation of China
- Shanghai Municipal Education Commission
- Shanghai University
- Fundamental Research Funds for the Central Universities
- Created
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2020-08-28Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field