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研究生： 譚登瑞
論文名稱： 空間各異性自旋二分之一海森堡模型之蒙地卡羅模擬
Monte Carlo simulation of 2-d spatially anisotropic spin-1/2 Heisenberg models
指導教授： 江府峻
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2012
畢業學年度： 100
語文別： 中文
論文頁數： 29
中文關鍵詞： 蒙地卡羅模擬 、海森堡模型 、相變
論文種類： 學術論文
相關次數： 點閱：156  下載：33 
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    • 本論文是使用Stochastic Series Expansion algorithm對2-d spatially anisotropic spin-1/2 Heisenberg models做Monte Carlo Simulation。在critical point附近，我們對所得到的ρ_s1 2L、ρ_s2 2L、Binder ratio Q_2、〈|m_s^z |〉及〈(m_s^z )^2 〉這五個物理量，利用finite-size scaling ansatz計算出critical exponent υ及β⁄υ，ρ_si為在晶格中i方向的spin stiffness，L為晶格邊界的大小，β為溫度的倒數，m_s^z為staggered magnetization的z分量，Q_2=〈(m_s^z )^2 〉^2⁄〈(m_s^z )^4 〉 。我們所模擬的model有staggered-dimer spin-1⁄2 Heisenberg model on the honeycomb lattice和ladder-dimer spin-1⁄2 Heisenberg model on square lattice，在結果上與近來提出需要較大的修正項的理論相容，並且和O(3) universality class的υ、β⁄υ及ω是一致的，但解釋這些數據結果仍需要更深刻的理論知識。

    前言......................................................1 Monte Carlo Simulation.....................................4 Stochastic Series Expansion方法............................5 Diagonal update............................................9 Loop update...............................................11 模型及觀測物理量............................................14 測定critical point及critical exponent.....................15 Honeycomb lattice上的staggered-dimer spin-1⁄2 Heisenberg model的結果...............................................16 Square lattice上的ladder-dimer spin-1⁄2 Heisenberg model的結果........................................................18 The calculation of the exponent β⁄υ.......................21 結論......................................................25 參考文獻...................................................27

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