论文标题
远程相互作用对D维ISING系统连接矩阵征收的变性的影响
Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system
论文作者
论文摘要
我们检查了ISING系统的连接矩阵，在线性尺寸的D维高立方体晶格上具有远程相互作用。我们将这些矩阵的特征向量表示为一维ISING系统的特征向量的Kronecker产品。连接矩阵的特征值是一维系统的特征值的d d级多项式。我们表明，包括远程相互作用在内不会消除连接矩阵特征值的退化。我们分析了限制中的特征值光谱密度为\ infty。在连续光谱的情况下，对于D <3，我们获得了分析公式，这些公式描述了远程相互作用对光谱密度和光谱的关键变化的影响。
We examine connection matrices of Ising systems with long-rang interaction on d-dimensional hypercube lattices of linear dimensions L. We express the eigenvectors of these matrices as the Kronecker products of the eigenvectors for the one-dimensional Ising system. The eigenvalues of the connection matrices are polynomials of the d-th degree of the eigenvalues for the one-dimensional system. We show that including of the long-range interaction does not remove the degeneracy of the eigenvalues of the connection matrix. We analyze the eigenvalue spectral density in the limit L go to \infty. In the case of the continuous spectrum, for d < 3 we obtain analytical formulas that describe the influence of the long-range interaction on the spectral density and the crucial changes of the spectrum.
