Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

doi:10.1103/PhysRevB.94.134424

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	Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT
	Huang, Wenxuan 1; Kitchaev, Daniil A.1; Dacek, Stephen T.1; Rong, Ziqin 1; Urban, Alexander 3; Cao, Shan 1; Luo, Chuan 2; Ceder, Gerbrand 1,3,4
刊名	PHYSICAL REVIEW B
	2016-10-21
卷号	94 期号:13 页码:12
ISSN号	2469-9950
DOI	10.1103/PhysRevB.94.134424
英文摘要	Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.
资助项目	US Department of Energy (DOE)[DE-FG02-96ER45571] ; Office of Naval Research[N00014-14-1-0444]
WOS研究方向	Physics
语种	英语
出版者	AMER PHYSICAL SOC
WOS记录号	WOS:000386092000002
内容类型	期刊论文
源URL	[http://119.78.100.204/handle/2XEOYT63/8010]
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Ceder, Gerbrand
作者单位	1.MIT, Dept Mat Sci & Engn, Cambridge, MA 02139 USA 2.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China 3.Univ Calif Berkeley, Dept Mat Sci & Engn, Berkeley, CA 94720 USA 4.Lawrence Berkeley Natl Lab, Div Mat Sci, Berkeley, CA 94720 USA
推荐引用方式 GB/T 7714	Huang, Wenxuan,Kitchaev, Daniil A.,Dacek, Stephen T.,et al. Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT[J]. PHYSICAL REVIEW B,2016,94(13):12.
APA	Huang, Wenxuan.,Kitchaev, Daniil A..,Dacek, Stephen T..,Rong, Ziqin.,Urban, Alexander.,...&Ceder, Gerbrand.(2016).Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT.PHYSICAL REVIEW B,94(13),12.
MLA	Huang, Wenxuan,et al."Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT".PHYSICAL REVIEW B 94.13(2016):12.