Study of Critical Phenomena in Low-Dimensional Magnets

低维磁体临界现象的研究

• 批准号: 08640445
• 负责人: TAKAHASHI Minoru
• 金额: $ 0.96万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640445/
• 关键词: Spin chain; Heisenberg model; Scaling; Magnetization curve; Ladder model; Dimer state; ダイヤー状態; 熱力学ベ-テ仮説方程式; スケーリング関数; 強磁性ハイゼンベルグ鎖; 反強磁性ハイゼンベルグ鎖; ボナ-フィッシャー曲線; 長距離相互作用

1. Critical phenomena of S=1 bond-altenating chain and analysis of experimental resultsS=1 antiferromagnetic chain has the energy gap. But it was expected that the alternating bond chain may become gapless at some strength of the alternation. We find that Ni(333-tet)(mu-N_3)(ClO_4)is such a chain with bond alternation. We did the Monte Carlo calculation and the exact diagonalization calculation and compared with experimental results by Hagiwara's group. The coincidence is very good.2. Study of spin systems with long range interactionProperties of the system with long-range interaction are quite different from those of systems with short-range interaction. Generally the short-range interacting spin systems have not phase transition in one and two dimensions. We investigated the low-temperature behavior of correlation length and phase transition of the system with long-range interaction using several approximations.3. Universal magnetic scaling function of ferromagnetic Heisenberg chainM … More agnetization curve of ferromagnetic Heisenberg model at low temperature approaches to some universal scaling function regardless to the fact that the system is classical or quantum. M=M<@D20phiM@>D2(<@D7P<@D2z@>D2H(/)T<@D12@>D1@>D7, <@D7P<@D2z@>D2(/)LT@>D7). Here rho<@D2s@>D2 is the stiffness constant, H is magnetic field, T is the temperature, L is the length of the system, M<@D20@>D2 is the saturation magnetization. We got phi<@D2M@>D2 (g, 0) = <@D72(/)3@>D7g - <@D744(/)135@>D7g<@D13@>D1 + <@D7752(/)2835@>D7g<@D15@>D1 - <@D7465704(/)1913625@>D7g<@D17@>D1 + <@D7356656(/)1515591@>D7g<@D19@>D1 - <@D7707126486624(/)3016973334375@>D7g<@D111@>D1 + <@D71126858624(/)4736221875@>D7g<@D113@>D1 - <@D75083735857217648(/)20771861407171875@>D7g<@D115@>D1 + ・・4. Numerical analysis of Anderson transiton in random magnetic fieldWe analyzed the critical exponents of Anderson transition in random magnetic field using the transfer matrix method. We certified the universality of the Anderson transition in the unitary class. Less

1、S=1键交替链的临界现象及实验结果分析S=1反铁磁链具有能隙。但预计交替键链在一定的交替强度下可能会变得无间隙。我们发现Ni(333-tet)(mu-N_3)(ClO_4)就是这样一条键交替的链。我们进行了蒙特卡罗计算和精确对角化计算，并与萩原课题组的实验结果进行了比较。巧合非常好。2。长程相互作用自旋系统的研究长程相互作用系统的性质与短程相互作用系统的性质有很大不同。一般来说，短程相互作用的自旋系统在一维和二维中不存在相变。我们利用多种近似方法研究了长程相互作用体系的相关长度和相变的低温行为。 3．铁磁海森堡链的通用磁标度函数M … 更多铁磁海森堡模型在低温下的磁化曲线接近于某个通用标度函数，无论系统是经典的还是量子的。 M=M<@D20phiM@>D2(<@D7P<@D2z@>D2H(/)T<@D12@>D1@>D7，<@D7P<@D2z@>D2(/)LT@>D7)。这里 rho<@D2s@>D2 是刚度常数，H 是磁场，T 是温度，L 是系统的长度，M<@D20@>D2 是饱和磁化强度。我们得到 phi<@D2M@>D2 (g, 0) = <@D72(/)3@>D7g - <@D744(/)135@>D7g<@D13@>D1 + <@D7752(/)2835@>D7g<@D15@>D1 - <@D7465704(/)1913625@>D7g<@D17@>D1 + <@D7356656(/)1515591@>D7g<@D19@>D1 - <@D7707126486624(/)3016973334375@>D7g<@D111@>D1 + <@D71126858624(/)4736221875@>D7g<@D113@>D1 - <@D75083735857217648(/)20771861407171875@>D7g<@D115@>D1 + ・・4。随机磁场中安德森跃迁的数值分析采用传递矩阵法对随机磁场中安德森跃迁的临界指数进行了分析。我们证明了安德森转变在单一类中的普遍性。较少的

项目成果

S.Takagi: "Magnetic Susceptibility of a Spin 1/2 Heisenberg Antiferromagnetic Chain" J.Phys.Soc.Jpn. 65. 1934-1937 (1996)

S.Takagi：“自旋 1/2 海森堡反铁磁链的磁化率”J.Phys.Soc.Jpn。

H.Nakano: "Long-Ranged Interacting Quantum Spin Chain with Exact Dimer State" J.Phys.Soc.Jpn. 66. 228-234 (1997)

H.Nakano：“具有精确二聚体状态的长程相互作用量子自旋链”J.Phys.Soc.Jpn。

M.Takahashi: "Conformal Field Theories and Integrable Models" Z.Horvath and L.Palla,Springer, 251 (1997)

M.Takahashi：“共形场论和可积模型”Z.Horvath 和 L.Palla，Springer，251 (1997)

M.Hagiwara: "Experimental Verification of the Gapless Point in the S=1 Antiferromagnetic Bond Alternating Chain" Phys.Rev.Lett.80. 1312-1315 (1998)

M.Hagiwara：“S=1 反铁磁键交替链中无间隙点的实验验证”Phys.Rev.Lett.80。

M.Takahashi: "Conformal Field Theories and Integrable Models" Z.Horvath and L.Palla, 251 (1997)

M.Takahashi：“共形场论和可积模型”Z.Horvath 和 L.Palla，251 (1997)