论文标题
精确解决方案类似于$ 2 \ times 2 \ times \ intispin互动型$ infty $型号
Exact solution Ising-like $2 \times 2 \times \infty$ models with multispin interactions
论文作者
论文摘要
本文认为，在$ 2 \ times2 \ times \ inty $ strip的$ 2 \ times 2 \ times \ infty $ strip中，对于通过角度$π/2 $旋转的中心旋转轴，其中包括单位单元中均匀数量的旋转的所有可能的乘积相互作用。对于围绕旋转旋转轴旋转的旋转轴的旋转轴的旋转轴的不变性，得出了非渗透概率的极限关系。通过转移矩阵方法获得溶液。在一般情况下，使用法拉利方法，找到$ 16 $ 16 $转移矩阵的最大特征值可以减少到四分之一的方程。在特殊情况下，使用辅助矩阵切换模型的传输矩阵使您可以将问题减少到二次和线性方程。在$ 2 \ times2 \ times \ infty $ strip中，单独的章节专门针对千禧年模型，对于自由边界条件的情况，在热力学限制中发现了自由能和热容量的确切值，并且在两个方向上循环旋转轴心持续的旋转边界条件的类似物。在自由边界条件的情况下，在循环闭合的情况下，将$ 3 \ times3 \ times \ times \ gonigendrial模型的数值解决方案与卷$ 2 \ times2 \ times \ times \ infty $中的相应分析解决方案进行了比较。显示了整个三维晶格的卫导型模型的热力学极限和热力学极限的亲密度，以及在$ 2 \ times2 \ times 2 \ times \ infty $ strip中的循环闭合的类似物。在$ 2 \ times2 \ times \ infty $ strive中，在热力学限制中的自由能和热量容量的确切值是针对抗磁性分层ISING模型获得的。
The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $π/2$, which includes all possible multiplicative interactions of an even number of spins in the unit cube.The exact value of free energy and heat capacity in the thermodynamic limit is found. For percolation invariant with respect to rotation about the central axis of rotation through the angle $π/2$, a limit relation for the non-percolation probability is derived. The solution was obtained by the transfer matrix method. In the general case, finding the largest eigenvalue of a $16 \times 16$ transfer matrix reduces to solving a quartic equation using the Ferrari method. In special cases, switching the transfer matrix of models with auxiliary matrices made it possible to reduce the problem to quadratic and linear equations. A separate chapter is devoted to the gonigendrial model in the $2\times2\times\infty$ strip, the exact values of the free energy and heat capacity in the thermodynamic limit are found for the case of free boundary conditions and an analogue of cyclically closed boundary conditions in both directions perpendicular to the central axis of rotation. The numerical solution for the $3\times3\times\infty$ gonigendrial model in the case of free boundary conditions and in the case of cyclic closure is compared with the corresponding analytical solutions in the volume $2\times2\times\infty$. The closeness of free energy and heat capacity in the thermodynamic limit for the gonigendrial model on the entire three-dimensional lattice and for the analog of cyclic closure in the $2\times2\times\infty$ strip is shown. The exact value of the free energy and heat capacity in the thermodynamic limit in the $2\times2\times\infty$ strip is obtained for the Antiferromagnetic layered Ising model.
