Zeros of ferromagnetic 2-spin systems

Heng Guo; Jingcheng Liu; Pinyan Lu

doi:10.1137/1.9781611975994.11

Zeros of ferromagnetic 2-spin systems

Heng Guo, Jingcheng Liu, Pinyan Lu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

Original language	English
Title of host publication	Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms
Pages	181-192
Number of pages	12
ISBN (Electronic)	978-1-61197-599-4
DOIs	https://doi.org/10.1137/1.9781611975994.11
Publication status	Published - 8 Jan 2020
Event	ACM-SIAM Symposium on Discrete Algorithms (SODA20) - Salt Lake City, United States Duration: 5 Jan 2020 → 8 Jan 2020 Conference number: 2020 https://www.siam.org/conferences/cm/conference/soda20

Conference

Conference	ACM-SIAM Symposium on Discrete Algorithms (SODA20)
Abbreviated title	SODA
Country/Territory	United States
City	Salt Lake City
Period	5/01/20 → 8/01/20
Internet address	https://www.siam.org/conferences/cm/conference/soda20

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title = "Zeros of ferromagnetic 2-spin systems",

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{\textquoteright}s and Ruelle{\textquoteright}s contraction method. The strength of our results is that they do not depend on the maximum degree of the underlying graph. Via Barvinok{\textquoteright}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",

author = "Heng Guo and Jingcheng Liu and Pinyan Lu",

year = "2020",

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doi = "10.1137/1.9781611975994.11",

language = "English",

pages = "181--192",

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AU - Lu, Pinyan

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Y1 - 2020/1/8

N2 - 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

AB - 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

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DO - 10.1137/1.9781611975994.11

M3 - Conference contribution

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BT - Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms

T2 - ACM-SIAM Symposium on Discrete Algorithms (SODA20)

Y2 - 5 January 2020 through 8 January 2020

ER -

Zeros of ferromagnetic 2-spin systems

Abstract

Conference

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