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:158 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。
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