簡易檢索 / 詳目顯示

回結果列表
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：148  下載：33 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 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

    [1] M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2001).
    [2] M. Troyer, Prog. Theor. Phys. Supp. 145, 326 (2002).
    [3] L.Wang, K. S. D. Beach, and A.W. Sandvik, Phys. Rev. B 73, 014431 (2006).
    [4] C. Yasuda et al., Phys. Rev. Lett. 94, 217201 (2005).
    [5] M. B. Hastings and C. Murdry, Phys. Rev. Lett. 96, 027215 (2006).
    [6] A. Praz, C. Murdy, and M. B. Hastings, Phys. Rev. B 74, 184407 (2006).
    [7] D. X. Yao and A. W. Sandvik, Phys. Rev. B 75, 052411(2007).
    [8] K. H. H¨oglund, A.W. Sandvik, and S. Sachdev, Phys. Rev. Lett. 98, 087203 (2007).
    [9] K. H. Hoglund and A.W. Sandvik, Phys. Rev. Lett. 99, 027205 (2007).
    [10] T. Pardini, R. R. P. Singh, A. Katanin and O. P. Sushkov, Phys. Rev. B 78, 024439 (2008).
    [11] F.-J. Jiang, F. K¨ampfer, and M. Nyfeler, Phys. Rev. B 80, 033104 (2009).
    [12] S. Jin and A. W Sandvik, arXiv:1110.5347.
    [13] J. Oitmaa, Y. Kulik, and O. P. Sushkov, arXiv:1110.6478.
    [14] S. Wenzel, L. Bogacz, and W. Janke, Phys. Rev. Lett. 101, 127202 (2008).
    [15] S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60, 1057 (1988).
    [16] F. D. M. Haldane, Phys. Rev. Lett. 61, 1029 (1988).
    [17] A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
    [18] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
    [19] M. Vojta, Rep. Prog. Phys. 66, 2069 (2003).
    [20] M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 65, 144520 (2002).
    [21] F.-J. Jiang, Rev. B 85 014414 (2012).
    [22] L. Fritz et al., Phys. Rev. B 83, 174416 (2011)
    [23] M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2001)
    [24] A. F. Albuquerque,M. Troyer, and J. Oitmaa, Phys. Rev. B 78, 132402 (2008).
    [25] S.Wenzel andW. Janke, Phys. Rev. B 79, 014410 (2009).
    [26] F.-J. Jiang and U. Gerber, J. Stat. Mech. P09016 (2009).
    [27] S. Wenzel, PhD thesis, Universita¨t Leipzig (2009).
    [28] H. G. Evertz, G. Lana, and M. Marcu, Phys. Rev. Lett. 70, 875 (1993).
    [29] H. G. Evertz, Adv. Phys. 52, 1 (2003).
    [30] U.-J. Wiese and H.-P. Ying, Z. Phys. B 93, 147 (1994).
    [31] B. B. Beard and U.-J. Wiese, Phys. Rev. Lett. 77 (1996) 5130.
    [32] A. F. Albuquerque et. al, Journal of Magnetism andMagnetic Material 310, 1187 (2007).
    [33] M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
    [34] E. Br´ezin, J. Phys. (Paris) 43, 15 (1982).
    [35] M. N. Barber, in Phase Transitions and Critical Phenomena, ed. C. Domb (Academic, New York, 1983), Vol. 8.
    [36] E. Br´ezin and J. Zinn-Justin, Nucl. Phys. B 257, 867(1985).
    [37] M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).

    下載圖示
    QR CODE