臺灣博碩士論文加值系統

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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