Study on the Magnetic Dilution in Quantum Spin Systems

(1)选择性磁稀释和位渗利用新有效场论（NEFT）对几种双亚晶格结构的晶格进行了选择性磁稀释研究。假设子晶格A和子晶格B被非磁性原子随机而选择性地稀释，保持稀释比U=(1-p_B)/(1-p_A)恒定，计算了T_C（p_A, p_B）的全局相图。结合T=OK时的相图，利用实空间重整化群论研究了该体系的选择性位点渗透，阐明了位点选择性U在研究初期渗透簇的关联长度指数和分形维数中的作用。(2)稀各向异性Heisenberg铁磁体的有效场论本文采用NEFT方法研究了稀各向异性Heisenberg铁磁体。居里回火的结果，更自然的T_C和磁有序的临界浓度，都是对单点近似的改进，而单点近似不能解释交换各向异性。随着晶格配位数和交换各向异性的增加，T_C随稀释的初始减少量也随之减少。(3)具有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推广到自旋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′变化时从各向异性Ising到各向同性Heisenberg行为的交叉。在D=0的各向同性情况下，我们严格地证明了，如果交换相互作用满足条件J'>J>0，则哈密顿量的基态在偶数位的连通有限晶格上总是单重态。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