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

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Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model, with two, three degenerate flavors (Nf = 2, 3) and two light plus one heavier flavor (Nf = 2 + 1). It is shown that in quark mass plane (mu/d − ms) 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 β and δ, 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 Nf = 2 and Nf = 3 respectively. For Nf = 2 + 1, in small strange quark mass (ms) 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 ms is larger than ms,t = 0.290 GeV, the dynamics of light flavors (u, d) and strange quarks decoupled and the critical exponents for ūu and overline{d}d becomes beta =frac{1}{2},delta =3 , exactly the same as Nf = 2 result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at ms,t = 0.290 GeV, at which beta =frac{1}{4},delta =5 . 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.