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We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field.
Shuai Shao and Yuxin Sun. Contraction: a unified perspective of correlation decay and zero-freeness of 2-spin systems. arXiv :1909.04244v1
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Alan D. Sokal. Bounds on the complex zeros of (di)chromatic polynomials and Potts-model partition functions. Combinatorics, Probability & Computing, 10(1):41-77, 2001
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Leslie A. Goldberg, Mark Jerrum and Mike Paterson. The computational complexity of two-state spin systems. Random Struct. Algorithms, 23(2):133-154, 2003
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Elias M. Stein and Rami Shakarchi. Complex Analysis. Princeton University Press, 2003
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Andrei A. Bulatov and Martin Grohe. The complexity of partition functions. Theoretical Computer Science, 348(2-3):148-186, 2005
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Alexander D. Scott and Alan D. Sokal. The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma. Journal of Statistical Physics, 118(5):1151-1261, 2005
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Dror Weitz. Counting independent sets up to the tree threshold. In proceedings of the thirty-eighth annual ACM symposium on theory of comouting, STOC 2006
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Martin E. Dyer, Leslie Ann Goldberg, and Mark Jerrum. The complexity of weighted boolean CSP. SIAM Journal on Computing 38(5):1970–1986, 2009
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Leslie A. Goldberg, Martin Grohe, Mark Jerrum, and Marc Thurley. A complexity dichotomy for partition functions with mixed signs SIAM Journal on Computing, 39(7):3336-3402, 2010
2010
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Allan Sly and Nike Sun. The computational hardness of counting in two-spin models on d d -regular graphs. Ann. Probab., 42(6):2383-2416, 2014
2014
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Alexander I. Barvinok Combinatorics and Complexity of Partition Function, volume 30 of Algorithms and combinatorics. Springer, 2016
2016
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Andreas Galanis, Daniel Štefankovič and Eric Vigoda. Inapproximability of the partition function for the antiferromagnetic Ising and hard-core models. Comb. Probab. Comput., 25(4):500-559, 2016
2016
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Jin-Yi Cai and Xi Chen. Complexity of counting CSP with complex weights, Journal of the ACM, 64(3):no.19, 2017
2017
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Viresh Patel and Guus Regts. Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials. SIAM J. Comput., 46(6):1893-1919, 2017
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2011
Cited alongside, same era.
2011
Cited alongside, same era.
Liang Li, Pinyan Lu and Yitong Yin. Approximate counting via correlation decay in spin systems. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
2012
Cited alongside, same era.
Andrei A. Bulatov. The complexity of the counting constraint satisfaction problem. Journal of the ACM 60(5):34:1–34:41, 2013
2013
Cited alongside, same era.
Jin-Yi Cai, Xi Chen, and Pinyan Lu. Graph homomorphisms with complex values: A dichotomy theorem. SIAM Journal on Computing 42(3):924–1029, 2013
2013
Cited alongside, same era.
Martin E. Dyer and David Richerby. An effective dichotomy for the counting constraint satisfaction problem. SIAM Journal on Computing 42(3):1245–1274, 2013
2013
Cited alongside, same era.
Liang Li, Pinyan Lu and Yitong Yin. Correlation decay up to uniqueness in spin systems. In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
2013
Cited alongside, same era.
Jin-Yi Cai, Pinyan Lu and Mingji Xia. The complexity of complex weighted Boolean #CSP. Journal of Computer and System Sciences, 80(1):217-236, 2014
2014
Cited alongside, same era.
2017
Later among the works it cites.
Alistair Sinclair, Piyush Srivastava, Daniel Štefankovič, and Yitong Yin. Spatial mixing and the connective constant: optimal bounds. Probab. Theory Related Fields, 168(1):153-197, 2017
2017
Later among the works it cites.
2018
Later among the works it cites.
Heng Guo and Pinyan Lu. Uniqueness, spatial mixing, and approximation for ferromagnetic 2-spin systems. ACM Trans. Comput. Theory, 10(4):Art 17, 25, 2018
2018
Later among the works it cites.
Nicholas J. A. Harvey, Piyush Srivastava, and Jan Vondrák. Computing the independence polynomial: from the tree threshold down to the roots. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
2018
Later among the works it cites.
2019
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Jingcheng Liu. Approximate counting, phase transitions and geometry of polynomials. Ph.D. Thesis, University of California, Berkeley, 2019
2019
Closest in time.
Jingcheng Liu, Alistair Sinclair, and Piyush Srivastava. Fisher zeros and correlation decay in the Ising model. In Proceedings of the Tenth Innovations in Theoretical Computer Science, ITCS 2019
2019
Closest in time.
Jingcheng Liu, Alistair Sinclair, and Piyush Srivastava. The Ising partition function: zeros and deterministic approximation. Journal of Statistical Physics, 174(2):287-315, 2019
2019
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Han Peters and Guus Regts. On a conjecture of sokal concerning roots of the independence polynomial. Michigan Math. J., 68(1):33-55, 2019
2019
Closest in time.