Lattice Field Theory with theta-term and Renormalization Group

研究了最大熵法（MEM）在带θ项的CP^{N-1}模型的负号问题中的作用。由于负号问题，自由能的依赖得到非光滑性。这种现象被称为“扁平化”。在这种情况下，MEM有时会表现出非平坦的光滑行为（m.i imachi, y.s inno和H.Yoneyama）。Prog.Theor.Phys。{111}第3号（2004）)。那么，在物理数据给出一阶相变的情况下，MEM是否会给出非光滑行为就出现了问题。这个问题在《原子核物理学》中有研究。(Proc.Suppl)。140(2005), 617-619（今町，信野和米山）。2)Azcoiti等人提出了将θ作为纯虚数处理的方法。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。我们使用的阿尔法芯片PC是由以前的资助和2003年推出的笔记本电脑（2003.9.1：笔记型PC (CLEVO 400)）和2004年由资助推出的两台台式电脑（PC (H17.2.25，桌面：Vip-HG 5330G/DVRDL， Vip-HG 5432P/DVRDL/GF66)）。这些机器进行了数值模拟。我们发现自由能作为h（=的虚部）的函数的逐步行为。虚θ的性质与有限密度QCD中的化学势问题密切相关。实际上，在有限密度QCD研究中也报告了类似的逐步行为，例如de Forcrand等人（Kratochvila和de Forcrand， help -lat/0409072, help -lat/0509143）。我们的结果总结在一篇论文help - late /0601028中（Imachi, Kmbayashi， Shinno和Yoneyama）。

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).