Abstract
各向異性海森堡模型的臨界性質周東川ABSTRACT///////We consider the spin-（圖表省略）anisotropic Heisenberg model described by the Hamiltonian（圖表省略）This hamiltonian corresponds to the Ising, Heisenberg and XY modelswhen（圖表省略）respectively. Exact high temperature series expansions are derived toorder T-7' for the second-order fluctuations and to order T-6 for thefourth-order fluctuations in the (ferromagnetic order parameters) for anarbitrary lattice, and are derived to T-7 for the secondorder fluctuationsin the antiferromagnetic order parameters for open lattices. These seriesare analysed by various methods to give the critical temperatures and thecritical exponents for all values of J∥and j┴.For a given lattice, when the anisotropy varies from the Ising limit(J┴=0) to the isotropic limit (│J∥│=│J┴│), the critical temperaturedecreases slowly (near zero slop) in the Ising limit and rapidly in theisotropic limit. Similar behavior is found when the system varies from theXY limit to the isotropic limit.For the cubic lattices our estimates of the critical exponents areconsistent with the universality hypothesis. The susceptibility exponentsγ for the cubic lattices and the staggered susceptibility exponents γNfor the bcc and sc lattices have the values γ（圖表省略）γN（圖表省略）1.38, 1.25, and 1.31 when the system is isotropic (J∥=│J┴│),Ising-like (│J┴│<│J∥│) and XY-like (│J∥│<│J┴│), respectively.For the cubic lattices we also find that the gap exponent △4=1.81, 1.56,ans 1.66 when 0<J┴=J∥,│J┴│<J∥, and │J∥│<J┴ respectively.For two-dimensional lattices, it is difficult to obtain reliable estimatesof the critical temperature from the series expansions for thesecond-order fluctuation, since the series coefficients are irregular inthe isotropic parameters, we find an evidence in favor of a phasetransition in the twodimensional lattices for all positive values of J∥and J1.