Computational complexity of spin-glass three-dimensional (3D) Ising model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909634627895296 |
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| author | Zhang, Zhidong |
| author_facet | Zhang, Zhidong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computational complexity of spin-glass three-dimensional (3D) Ising model Zhang, Zhidong General Physics 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. |
| title | Computational complexity of spin-glass three-dimensional (3D) Ising model |
| topic | General Physics |
| url | https://arxiv.org/abs/2506.02067 |