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#### Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

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1810.07019.pdf

(Preprint), 648KB

JHEP2019_01_165.pdf

(Publisher version), 1005KB

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##### Citation

Chen, J., He, S., Huang, M., & Li, D. (2019). Critical exponents of finite temperature
chiral phase transition in soft-wall AdS/QCD models.* Journal of High Energy Physics,* *2019*(01): 165. doi:10.1007/JHEP01(2019)165.

Cite as: https://hdl.handle.net/21.11116/0000-0002-6D40-C

##### Abstract

Criticality of chiral phase transition at finite temperature is investigated

in a soft-wall AdS/QCD model with $SU_L(N_f)\times SU_R(N_f)$ symmetry,

especially for $N_f=2,3$ and $N_f=2+1$. It is shown that in quark mass

plane($m_{u/d}-m_s$) chiral phase transition is second order at a certain

critical line, by which the whole plane is divided into first order and

crossover regions. The critical exponents $\beta$ and $\delta$, describing

critical behavior of chiral condensate along temperature axis and light quark

mass axis, are extracted both numerically and analytically. The model gives the

critical exponents of the values $\beta=\frac{1}{2}, \delta=3$ and

$\beta=\frac{1}{3}, \delta=3$ for $N_f=2$ and $N_f=3$ respectively. For

$N_f=2+1$, in small strange quark mass($m_s$) region, the phase transitions for

strange quark and $u/d$ quarks are strongly coupled, and the critical exponents

are $\beta=\frac{1}{3},\delta=3$; when $m_s$ is larger than

$m_{s,t}=0.290\rm{GeV}$, the dynamics of light flavors($u,d$) and strange

quarks decoupled and the critical exponents for $\bar{u}u$ and $\bar{d}d$

becomes $\beta=\frac{1}{2},\delta=3$, exactly the same as $N_f=2$ result and

the mean field result of 3D Ising model; between the two segments, there is a

tri-critical point at $m_{s,t}=0.290\rm{GeV}$, at which

$\beta=0.250,\delta=4.975$. In some sense, the current results is still at mean

field level, and we also showed the possibility to go beyond mean field

approximation by including the higher power of scalar potential and the

temperature dependence of dilaton field, which might be reasonable in a full

back-reaction model. The current study might also provide reasonable

constraints on constructing a realistic holographic QCD model, which could

describe both chiral dynamics and glue-dynamics correctly.

in a soft-wall AdS/QCD model with $SU_L(N_f)\times SU_R(N_f)$ symmetry,

especially for $N_f=2,3$ and $N_f=2+1$. It is shown that in quark mass

plane($m_{u/d}-m_s$) chiral phase transition is second order at a certain

critical line, by which the whole plane is divided into first order and

crossover regions. The critical exponents $\beta$ and $\delta$, describing

critical behavior of chiral condensate along temperature axis and light quark

mass axis, are extracted both numerically and analytically. The model gives the

critical exponents of the values $\beta=\frac{1}{2}, \delta=3$ and

$\beta=\frac{1}{3}, \delta=3$ for $N_f=2$ and $N_f=3$ respectively. For

$N_f=2+1$, in small strange quark mass($m_s$) region, the phase transitions for

strange quark and $u/d$ quarks are strongly coupled, and the critical exponents

are $\beta=\frac{1}{3},\delta=3$; when $m_s$ is larger than

$m_{s,t}=0.290\rm{GeV}$, the dynamics of light flavors($u,d$) and strange

quarks decoupled and the critical exponents for $\bar{u}u$ and $\bar{d}d$

becomes $\beta=\frac{1}{2},\delta=3$, exactly the same as $N_f=2$ result and

the mean field result of 3D Ising model; between the two segments, there is a

tri-critical point at $m_{s,t}=0.290\rm{GeV}$, at which

$\beta=0.250,\delta=4.975$. In some sense, the current results is still at mean

field level, and we also showed the possibility to go beyond mean field

approximation by including the higher power of scalar potential and the

temperature dependence of dilaton field, which might be reasonable in a full

back-reaction model. The current study might also provide reasonable

constraints on constructing a realistic holographic QCD model, which could

describe both chiral dynamics and glue-dynamics correctly.