铁磁性三维Ising模型精确解及时间的自发产生

张志东

Exact Solution of Ferromagnetic Three-Dimensional (3D) Ising Model and Spontaneous Emerge of Time

ZHANG Zhidong

图5 三维Ising模型一个晶格单胞示意图[22]

Fig.5 Schemes illustrate a unit cell of the 3D cubic Ising lattice[22] (All the five figures can be mapped each other, in which there are two contributions to physical properties: one is local spin alignment, another is nonlocal effect of the braids) (a) with spins (red arrows) located at every lattice site and braids (blue curves) attached to every pair of the two nearest neighboring lattice sites along the third dimension (b) with spins (red arrows) located at every lattice site and spin chains (black arrows with blue curves) formed by the mapping from the nontrivial knots (nonlinear terms) (c) with crossings (red curves) are mapped from spins in a unit cell of the 3D Ising lattice, and some crossings (blue curves) are attached braids from the nontrivial topological structure (d) a unit cell of the (3 + 1)D hypercubic Ising lattice in which the spins on the original 3D Ising lattice (black lines) are represented by red arrows and the spins in the high dimensional lattice (blue lines) are represented by black arrows (e) a example of knots with crossings located on a unit cell of the (3 + 1)D hypercubic Ising lattice.