THEORETICAL STUDY OF EXCHANGE INTERACTION, PARTICULARLY, OF MULTIPLE-SPIN EXCHANGE INTERACTION.

(1)我成功地开发了一种利用WKB方法（瞬时法）和数值计算计算交换相互作用常数的方法。此方法可以比WKB方法更精确地计算交换常数。(2)我首次将这种方法应用于二维维格纳晶体，发现多自旋交换在这一阶段确实有效。我还研究了磁场对交换过程的影响，发现磁场通过Aharanov-Bohm效应对交换常数产生非平凡的影响，并能在场中得到二维维格纳晶体丰富的相图。研究了双层维格纳晶体相的自旋交换，发现只要两层之间的距离远小于粒子间的平均距离，该相的磁性可以用一维反铁磁海森堡模型很好地描述。(3)采用WKB方法研究了衬底电位对石墨吸附单层固体氦3交换过程的影响。发现底物电位对稀区交换过程有严重影响，导致交换常数的密度依赖性与浓区交换常数的密度依赖性完全不同。

(1) I have successfully developed a method of calculating exchange interaction constants using the WKB method (the instanton method) and the numerical calculation. This method can make it possible to calculate the exchange constants much more precisely than ever within the WKB method. (2) I have first applied this method to the two-dimensional Wigner crystal and found that multiple-spin exchanges really work in this phase. I have also studied the effect of a magnetic field on the exchange processes and found that the field affects the exchange constants in a non-trivial way through the Aharanov-Bohm effect and can bring about a rich phase diagram of the two-dimensional Wigner crystal in a field. Spin exchange in a bilayer Wigner crystal phase is also studied, and it is found that the magnetic properties of this phase is welll described by the one-dimensional antiferriomagnetic Heisenberg model as long as the distance between the two layers is much smaller than the average interparticle distance. (3) The effect of the substrate potential on the exchange processes in the monolayer solid Helium 3 adsorbed on graphite is also studied using the WKB method. It is found that the substrate potential seriously affects the exchange processes in the dilute case, and brings about the density dependence of the exchange constants that is completely different from the dependence in the dense region.