长程相互作用对d维伊辛系统联系矩阵特征值简并度的影响
Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system
摘要：
研究了线性维数为L的d维超立方体格上具有长程相互作用的Ising系统的连接矩阵。我们将这些矩阵的特征向量表示为一维伊辛系统的特征向量的克罗内克积。连接矩阵的特征值是一维系统的特征值的第d次多项式。我们表明，包括长程相互作用并没有删除的连接矩阵的本征值的退化。我们分析了极限L到\infty的特征值谱密度。在连续谱的情况下，当d < 3时，我们得到了描述长程相互作用对谱密度的影响和谱的关键变化的解析公式。
英文摘要：
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.
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