Roberge-Weiss transition endpoints with Wilson and improved KS quarks

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Presentation transcript:

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

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

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)

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)

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

Second order line Triple line Tricritical point

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

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

Imaginary part of Polyakov loop taken as order parameter （H.Kouno,et al., J.Phys.G36 ,115010 (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)

0.155 0.160 0.165 0.168 0.170 0.175 0.180 0.190 0.198

0.020 0.040 0.060 0.070 0.080 0.100 0.120

3D Ising 0.6301(4) 1.2372(5) 1.963 Tricritical 0.5 1 2 First order 0.3 1 3 A.Pelissetto and E.Vicari, Phys.Rep.,368,549(2002) crossover triple point second order tricritical point 3 1.5 1.604 2 P.de Forcrand and O.Philipsen, Phys.Rev.Lett., 105,152001(2010)

0.020 0.040 0.060 0.070 0.080 0.100 0.120 0.140 0.155 0.160 0.165 0.168 0.170 …. Second order points Tricritical point Triple points Triple points O.Philipsen and C.Pinke, PRD 89,094504(2014)

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

三 Improved action Error of lattice spcaing： A.Bazavov, et al., Rev.Mod.Phys.,82 1349(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)

1 -1/24 1/16 1/64 1/384 -1/8 A.Bazavov, et al., Rev.Mod.Phys.,82 1349(2010) and Refs. thereof

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：

am 0.024 0.026 0.038 0.040 0.050 0.060 0.070

am=0.050 0.060 am=0.038 0.040 0.070

Tricritical point 3D Ising 0.6301(4) 1.2372(5) 1.963 First order 0.3 1 3 am 0.024 0.026 0.038 0.040 0.050 0.060 0.070 Tricritical point

Discussion: Data points are not enough Two lattice volumes some intersections are obtained from two spatial volumes 3) From 0.024 to 0.026，change of critical index is rapid 4) Region between Tricritical points is narrow. arXiv:1612.03384 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)

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！

3D Ising 0.6301(4) 1.2372(5) 1.963 Tricritical 0.5 1 2 First order 0.3 1 3 A.Pelissetto and E.Vicari, Phys.Rep.,368,549(2002) crossover triple point second order tricritical point 3 1.5 1.604 2 P.De Forcrand and O.Philipsen, Phys.Rev.Lett., 105,152001(2010)

Z(3) 相变在虚化学势下温度增大虚化学势增大

温度增大 Triple line

First order 温度增大化学势增大 crossover Tricritical point Tricritical point

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

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: