1. Roberge-Weiss transition endpoints with Wilson and improved KS quarks
Faculty of Science, Jiangsu University Liang-Kai Wu

2. 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

3. RHIC (Relativistic Heavy Ion Collider) LHC (Large Hadron Collider)
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RHIC (Relativistic Heavy Ion Collider)
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4. 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)

5. 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

6. Second order line
Triple line
Tricritical point

7. Second order line Tricritical point Triple line
Figure from PRD 90,074030

8. 二 Simulation with Wilson fermions
partition function：
Gauge action： ，而
Fermion action：
Fermion matrix M：

9. 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)

15. 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)

16. ….
Second order points
Tricritical point
Triple points
Triple points
O.Philipsen and C.Pinke, PRD 89,094504(2014)

17. 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

18. 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)

19. 1
-1/24
1/16
1/64
1/384
-1/8
A.Bazavov, et al., Rev.Mod.Phys., (2010) and Refs. thereof

20. 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：

21. am

22. am=
am=

24. Tricritical point 3D Ising 0.6301(4) 1.2372(5) 1.963
First order am
Tricritical point

25. 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)

26. 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！

27. 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)

28. Z(3) 相变
在虚化学势下
温度增大
虚化学势增大

30. 温度增大
Triple line

32. First order
温度增大
化学势增大
crossover
Tricritical point
Tricritical point

33. 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

34. 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: