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

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.Comment: 32 pages, 11 figures, regular articl

Adaptive Channel Recommendation For Opportunistic Spectrum Access

We propose a dynamic spectrum access scheme where secondary users recommend "good" channels to each other and access accordingly. We formulate the problem as an average reward based Markov decision process. We show the existence of the optimal stationary spectrum access policy, and explore its structure properties in two asymptotic cases. Since the action space of the Markov decision process is continuous, it is difficult to find the optimal policy by simply discretizing the action space and use the policy iteration, value iteration, or Q-learning methods. Instead, we propose a new algorithm based on the Model Reference Adaptive Search method, and prove its convergence to the optimal policy. Numerical results show that the proposed algorithms achieve up to 18% and 100% performance improvement than the static channel recommendation scheme in homogeneous and heterogeneous channel environments, respectively, and is more robust to channel dynamics