Exact Solution of Ferromagnetic Three-Dimensional (3D) Ising Model and Spontaneous Emerge of Time
Received date: 2022-10-08
Revised date: 2022-12-30
Online published: 2023-01-11
Supported by
National Natural Science Foundation of China(52031014)
This article reviews recent advances in the exact solution of ferromagnetic three-dimensional (3D) Ising model. First, the topological quantum statistic mechanism was introduced, which includes the time average, Jordan-von Neumann-Wigner framework, and the contribution of topological structures to thermodynamic properties of the system. Then, the Clifford algebra approach and the method of the Riemann-Hilbert problem were introduced to prove Zhang's two conjectures for the exact solution of the ferromagnetic 3D Ising model. The proof process verifies the correctness of the Zhang's exact solution for the ferromagnetic 3D Ising model. Based on these progresses, the origin of time was investigated and driven to the conclusion that in 3D many-body interacting particle (or spin) systems, time emerges spontaneously from many-body interactions.
ZHANG Zhidong . Exact Solution of Ferromagnetic Three-Dimensional (3D) Ising Model and Spontaneous Emerge of Time[J]. Acta Metall Sin, 2023 , 59(4) : 489 -501 . DOI: 10.11900/0412.1961.2022.00486
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