Study on the Magnetic Dilution in Quantum Spin Systems

(1)选择性磁稀释与格位渗流用新有效场理论（NEFT）研究了几种双子格结构晶格上的选择性磁稀释。假设子格A和B被非磁性原子随机但选择性地稀释，稀释比U=（1-p_B）/（1-p_A）保持不变，计算了T_C（p_A，p_B）的全局相图。结合T=OK时的相图，用真实的空间重整化群理论研究了该体系的选择性位渗流，阐明了位选择性U在研究初渗流团簇的关联长度指数和分形维数中的作用。(2)稀磁各向异性海森伯铁磁体的有效场论本文用NEFT方法研究了稀磁各向异性海森伯铁磁体，在两格点集团近似下，假设周围的自旋具有Ising特征。居里温度的结果 关于我们 温度、T_C和磁有序的临界浓度是对不能考虑交换各向异性的单格位近似的改进。T_C随稀释的初始降低被证实随晶格配位数和交换各向异性的增加而减小。(3)单离子单轴各向异性的双线性-双二次量子交换模型上述计算已扩展到自旋S=1的系统，包括双二次交换相互作用J'和单离子各向异性D。特别地，我们研究了T_C随强度J'的变化中各向异性Ising到各向同性Heisenberg行为的交叉。并讨论了在一定强度D范围内临界浓度附近出现的假重入相变现象。对于D=0的各向同性情形，我们严格地证明了在偶数格点的有限连通格点上，如果交换作用满足条件J '> J>0，则哈密顿量的基态总是单态的.少

(1) Selective Magnetic Dilution and Site PercolationThe selective magnetic dilution has been studied by the new effective field theory (NEFT) on the lattices with several kinds of two-sublattice structures. Sublattices A and B are assumed to be randomly but selectively diluted by non magnetic atoms, keeping dilution ratio U=(1-p_B)/(1-p_A) constant, and the global phase diagrams of T_C(p_A, p_B) has been calculated. In conjunction with the phase diagram at T=OK,we investigated selective site percolation of this system by real space renormalization group theory and clarified the role of site selectivity U in the study of thecorrelation length exponent and the fractal dimension of the incipient percolation cluster.(2) An Effective Field Theory for Dilute Anisotropic Heisenberg FerromagnetsDilute anisotropic Heisenberg ferromagnets have been studied by NEFT based on a two-site cluster approximation with an Ising character assumed for the surrounding spins. The results for the Curie temper … More ature, T_C, and the critical concentration for magnetic ordering are improvements on those of a single-site approximation where the exchange anisotropy cannot be accounted for. The initial reduction in T_C with dilution has been confirmed to decrease with increase in both the lattice coordination number and exchange anisotropy.(3) Bilinear-Biquadratic Quantum Exchange Model with Single-Ion Uniaxial AnisotropyThe above calculation has been extended to the system of spin S=1, including biquadratic exchange interaction J' and single ion anisotropy D.In particular, we studied the cross-over from anisotropic Ising to isotropic Heisenberg behavior in the variation of T_C with strength J', and also discussed about a spurious reentrant transition phenomena which is found in the vicnity of the critical concentration over a range of strength D.For the isotropic case of D=0, we showed rigorously that the ground state of the Hamiltonian is always singlet on a connected finite lattice with an even number of site, if the exchange interactions satisfy the condition J'>J>0. Less