臺灣博碩士論文加值系統

在本篇論文中，我們以集團平均場近似針對同時具有近鄰與次近鄰交互作用的自旋 1/2 XXZ 海森堡模型去計算當系統處於基態時的自旋長程序。我們控制住近鄰與次近鄰兩種交互作用的強度比例，並調變自旋角動量間耦合作用的空間異向性來追蹤系統的相變行為，觀察相變發生的條件與集團大小的縮放之間是否存在良好的關聯性。

In this paper, we employ the cluster mean-field theory to find out the ordering phases of the spins in the ground state of the spin 1/2 XXZ Heisenberg model which possess both interaction between nearest neighbor and between next nearest neighbor. We fix the strength ratio of between these two interaction, and adjust the space anisotropy of the spin angular momentum coupling to trace if the critical point can show fine scaling behavior.

誌謝 i
中文摘要 iii
英文摘要 iv
目錄 v
表目錄 vii
圖目錄 ix
第一章　緒論 1
第二章　模型 4
2.1 海森堡模型 4
2.2 集團平均場近似 10
第三章　數值方法 20
3.1 雙自旋 12 系統 20
3.2 Lanczos方法 24
3.3 序參數 28
第四章　研究結果 32
4.1 長程序的轉向 32
4.2 集團平均場近似的外推法 38
第五章　討論 43
參考文獻 45

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