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Roberge-Weiss transition endpoints with Wilson and improved KS quarks
Faculty of Science, Jiangsu University Liang-Kai Wu
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Outline 1) Roberge-Weiss transition endpoint
2)Simulation with Wilson fermion formulation 3)Symanzik improved gauge action and Asqtad fermion action 4)Results with improved action
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RHIC (Relativistic Heavy Ion Collider) LHC (Large Hadron Collider)
Evolution of Universe Compact stars RHIC (Relativistic Heavy Ion Collider) LHC (Large Hadron Collider) SPS (Super Proton Synchrotron)
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一 Roberge-Weiss transition endpoints
Partition function: Pure gauge theory: Z(3) symmetry QCD: Z(3) symmetry is broken QCD: real chemical potential imaginary chemical potential, Z(3) is restored With imaginary chemical potential,system is periodic, partition function is even function of chemical potential Nucl.phys.,B275,734(1986)
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At high temperature :first order transition
Critical value: At high temperature :first order transition At low temperature : crossover First order crossover Chemical potential increases Temperature increases Different Z(N) sectors
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Second order line Triple line Tricritical point
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Second order line Tricritical point Triple line
Figure from PRD 90,074030
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二 Simulation with Wilson fermions
partition function: Gauge action: ,而 Fermion action: Fermion matrix M:
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Imaginary part of Polyakov loop taken as order parameter
(H.Kouno,et al., J.Phys.G36 , (2009)). Polyakov loop: Susceptibility: Susceptibility scaling behaviour: C.Bonati, etal., Phys.Rev., D83,054505(2011) Binder cumulant : Binder cumulant scaling behaviour : P.de Forcrand and O.Philipsen, Phys.Rev.Lett., 105,152001(2010)
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3D Ising (4) (5) Tricritical First order A.Pelissetto and E.Vicari, Phys.Rep.,368,549(2002) crossover triple point second order tricritical point P.de Forcrand and O.Philipsen, Phys.Rev.Lett., 105,152001(2010)
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…. Second order points Tricritical point Triple points Triple points O.Philipsen and C.Pinke, PRD 89,094504(2014)
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Scenario 2 first order Scenario 1 second order Triple line
Tricritical point Tricritical point Second order line Scenario 2 first order Scenario 1 second order
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三 Improved action Error of lattice spcaing:
A.Bazavov, et al., Rev.Mod.Phys., (2010) M,Luscher and P.Weisz, Phys.lett.,B158,250(1985), Commun.math.phys.,97,59(1985); Z.Hao, et al., PRD, 76,034507(2007)
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1 -1/24 1/16 1/64 1/384 -1/8 A.Bazavov, et al., Rev.Mod.Phys., (2010) and Refs. thereof
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RHMC (rational hybrid Monte Carlo algorithm) :
M.A.Clark and A.D.Kennedy, PRD 75,011502(2007);PRL,98,051601(2007) Heat baths: Fermion action: Molecular dynamic:
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am
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am= am=
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Tricritical point 3D Ising 0.6301(4) 1.2372(5) 1.963
First order am Tricritical point
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Discussion: Data points are not enough
Two lattice volumes some intersections are obtained from two spatial volumes 3) From to 0.026,change of critical index is rapid 4) Region between Tricritical points is narrow. arXiv: 0.043(5) 0.72(8) C.Bonati, etal., PRD 83,054505(2011) 0.07<am<0.3 0.5<am<1.5 P.de Forcran and O.Philipsen, PRL,105,152001(2010)
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谢谢大家! Thanks to Philippe de Forcrand, Chuan Liu
And Wang Qiong, Zhao Liu in Supercomputer Center in Wuxi 谢谢大家!
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3D Ising (4) (5) Tricritical First order A.Pelissetto and E.Vicari, Phys.Rep.,368,549(2002) crossover triple point second order tricritical point P.De Forcrand and O.Philipsen, Phys.Rev.Lett., 105,152001(2010)
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Z(3) 相变 在虚化学势下 温度增大 虚化学势增大
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温度增大 Triple line
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First order 温度增大 化学势增大 crossover Tricritical point Tricritical point
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5) Z(3) 相变 在虚化学势下 不同的Z(N)区 温度增大 曲线的表达式的形式 ? 虚化学势增大
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Roberge-Weiss相变 配分函数: 纯规范场: Z(3) 对称性 QCD: Z(3) 对称性破缺
高温下:一阶相变 低温下:crossover Critical value:
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