Lattice Field Theory with theta-term and Renormalization Group

具有 theta 项和重正化群的格场论

• 批准号: 15540249
• 负责人: IMACHI Masahiro
• 金额: $ 1.34万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540249/
• 关键词: Lattice Field Theory; CP^{N-1}; Theta term; Complex Boltzmann Factor; Maximum Entropy Method; Topological Charge Distribution; Pure Imaginary theta; Finite Density QCD; 複数ボルツマン因子; トポロジカル荷電; CP^N-1場の理論; フラットニング; 純虚数テータパラメータ; 数値実験; CP^<N-1>模型

We investigated the role of MEM (Maximum Entropy Method) on the problem of negative sign problem in the CP^{N-1} model with theta-term. Theta -dependence of free energy obtains non smooth behavior due to negative sign problem. This phenomena is called "flattening". In such case, MEM sometimes shows non-flat smooth behavior (M.Imachi, Y.Shinno and H.Yoneyama. Prog.Theor.Phys. {111} No.3 (2004)). Then there appears the question that whether MEM will give non-smooth behavior, insuch a case where physical data gives the first order phase transition. This problem is investigated in Nucl.Phys. (Proc.Suppl.) 140 (2005), 617-619 (Imachi, Shinno and Yoneyama).2)Azcoiti et al proposed the method to treat theta as pure imaginary. They applied the method to strong coupling region. We studied the weak coupling region of CP^{2} model. We used alpha chip PC's which are introduced by previous grant and notebook PC introduced in 2003 (2003.9.1 : note PC (CLEVO 400)) and two desktop PC's introduced in 2004 by grant (PC (H17.2.25, Desktop : Vip-HG 5330G/DVRDL, Vip-HG 5432P/DVRDL/GF66)). Numerical simulation is performed by these machines. We found stepwise behavior of free energy as a function of h (= imaginary part of theta). The property of imaginary theta is closely related to the problem of chemical potential in finite density QCD. Actually similar stepwise behavior is reported in finite density QCD studies e.g. by de Forcrand et al (Kratochvila and de Forcrand, hep-lat/0409072, hep-lat/0509143). Our result is summarised in a paper hep-lat/0601028, (by Imachi, Kmbayashi, Shinno and Yoneyama).

我们研究了MEM（最大熵方法）对使用Theta-Term的CP^{N-1}模型中负符号问题问题的作用。由于负符号问题，自由能的依赖性依赖性可获得非平滑行为。这种现象称为“平坦”。在这种情况下，MEM有时会显示出非平稳的行为（M.Imachi，Y.Shinno和H.Yoneyama。prog.theor.phys。{111} No.3（2004））。然后，似乎有一个问题，即MEM是否会提供非平滑行为，这是物理数据给出一阶相变的情况。该问题在nucl.phys中进行了研究。 （Proc.Suppl。）140（2005），617-619（Imachi，Shinno和Yoneyama）.2）Azcoiti等人提出了将Theta视为纯虚构的方法。他们将该方法应用于强耦合区域。我们研究了Cp^{2}模型的弱耦合区域。我们使用了Alpha Chip PC，由以前的赠款和笔记本电脑在2003年推出（2003.9.1：Note PC（CLEVO 400））和两个台式PC在2004年由Grant推出（H17.2.25，桌面：VIP-HG 5330G 5330G/DVRDL，VIP-HG 5432P/dvrdl/dvrdl/dvrdldl/dvrdl/gffrdldl/dldl/grant介绍。数值模拟由这些机器执行。我们发现自由能的逐步行为与h（= theta的假想部分）的函数。假想theta的特性与有限密度QCD中的化学势问题密切相关。实际上在有限密度QCD研究中报告了类似的逐步行为，例如De Forcrand等人（Kratochvila和de Forcrand，Hep-Lat/0409072，Hep-Lat/0509143）。我们的结果总结在纸hep-lat/0601028中（由imachi，kmbayashi，shinno和yoneama）进行了总结。

项目成果

APPLICATION OF MAXIMUM ENTROPY METHOD TO LATTICE FIELD THEORY WITH A TOPOLOGICAL TERM

最大熵法在拓扑项格子场论中的应用

• 发表时间: 2004
• 期刊: Nucl.Phys.(Proc.Suppl.) 129
• 作者: M.Imachi;Y.Shinno;H.Yoneyama;S.Aoki;S.Aoki;井町昌弘;T.Kaneko;M.Imachi;T.Kaneko;M.Imachi
• 通讯作者: M.Imachi

MEM study of true flattening of free energy and the theta term

自由能真实平坦化和 theta 项的 MEM 研究

• 发表时间: 2005
• 期刊: Nucl. Phys. (Proc. Suppl.) 140
• 作者: S.Takeda;S.Aoki;et al.;S.Takeda;S.Aoki;S.Aoki;S.Takeda;井町昌弘
• 通讯作者: 井町昌弘

M.Imachi他: "Maximal Entrogy Method Approach to the θ Term"Prog.Theor.Phys.. 111・3. (2004)

M. Imachi 等：“θ 项的最大熵方法”Prog.Theor.Phys.. 111・3。

MAXIMUM ENTROPY METHOD APPROACH TO THETA TERM

Theta 项的最大熵方法

• 发表时间: 2004
• 期刊: Prog.Theor.Phys. 111・3
• 作者: S.Takeda;S.Aoki;et al.;M.Imachi
• 通讯作者: M.Imachi