Journal
JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY
Volume 44, Issue -, Pages 116-120Publisher
JOURNAL MATER SCI TECHNOL
DOI: 10.1016/j.jmst.2019.12.009
Keywords
3D Ising model; Spin-glass; Computational complexity
Funding
- National Natural Science Foundation of China [51590883, 51331006]
- State Key Project of Research and Development of of China [2017YFA0206302]
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In this work, the computational complexity of a spin-glass three-dimensional (3D) Ising model (for the lattice size N= lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that an absolute minimum core (AMC) model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane, has its computational complexity O(2(mn)). Any algorithms to make the model smaller (or simpler) than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model. Therefore, the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2(mn)) by any algorithms, which is in subexponential time, superpolynomial. (C) 2020 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
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