论文标题
轴向下一个最邻居的ISING模型的确切解决方案2旋转链
The exact solution of the Axial Next-Nearest-Neighbor Ising model on width 2 spin chains
论文作者
论文摘要
Using the transfer matrix method for Axial Next-Nearest Neighbor Ising model without an external field on a closed chain of spins of width 2 in the direction of interaction of only nearest neighbors and length L in the direction of interaction of nearest neighbors and next nearest neighbors, we found exact values of the partition function in a finite strip of length L , free energy, internal energy per node, heat capacity in a finite strip of length L and in the thermodynamic limit.发现16x16转移矩阵的整个光谱和所有转移矩阵特征向量的结构。找到转移矩阵的频谱的问题减少到找到两个尺寸8x8的矩阵的频谱。第一个矩阵的特征多项式分解为两个和两个平方三项元素的两个线性多项式。第二矩阵的特征多项式分解为第四级的两个多项式，其根是通过法拉利方法发现的。热力学极限中的自由能具有非常简单的形式，并以二次方程根的对数表示。在有限的长度L和热力学极限中，在Annni模型的物理特征上进行了两个定理，并证明了。在热力学极限中给出了一些模型参数值的计算示例，绘制了热容量图。对整个平面晶格的双链Annni模型和Annni模型的热容量进行了比较分析。显示了两链模型的物理特征的最接近的连接和相似性和整个平面晶格上的模型。
Using the transfer matrix method for Axial Next-Nearest Neighbor Ising model without an external field on a closed chain of spins of width 2 in the direction of interaction of only nearest neighbors and length L in the direction of interaction of nearest neighbors and next nearest neighbors, we found exact values of the partition function in a finite strip of length L , free energy, internal energy per node, heat capacity in a finite strip of length L and in the thermodynamic limit. The entire spectrum of the 16x16 transfer matrix and the structure of all transfer matrix eigenvectors are found. The problem of finding the spectrum of the transfer matrix is reduced to finding the spectrum of two matrixes of size 8x8. The characteristic polynomial of the first matrix is decomposed into two linear polynomials of multiplicity two and two square trinomials. The characteristic polynomial of the second matrix is decomposed into two polynomials of the fourth degree, the roots of which are found by the Ferrari method. The free energy in the thermodynamic limit has a very simple form and is expressed in terms of the logarithm of the root of the quadratic equation. Two theorems on the physical characteristics of the ANNNI model in a finite closed strip of length L and in the thermodynamic limit are formulated and proved. An example of calculation is given for some values of the model parameters in the thermodynamic limit, heat capacity graphs are plotted. A comparative analysis of the heat capacity for the double-stranded ANNNI model and the ANNNI model on the entire flat lattice is given. The closest connection and similarity of the physical characteristics of the two-chain model and the model on the entire flat lattice is shown.
