2005 Fiscal Year Final Research Report Summary
Lattice Field Theory with theta-term and Renormalization Group
| Project/Area Number |
15540249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Yamagata University |
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Principal Investigator |
IMACHI Masahiro Yamagata Univ., Department of Physics, Professor, 理学部, 教授 (70037208)
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| Co-Investigator(Kenkyū-buntansha) |
YONEYAMA Hiroshi Saga Univ., Department of Physics, Professor, 理工学部, 教授 (50210795)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Lattice Field Theory / CP^{N-1} / Theta term / Complex Boltzmann Factor / Maximum Entropy Method / Topological Charge Distribution / Pure Imaginary theta / Finite Density QCD |
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| Research Abstract |
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).
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Research Products
(2 results)
