We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For the dilaton we take a quadratic ansatz leading to linear confinement at zero temperature and density. We consider a grand canonical ensemble, where the chemical potential is fixed, and find a rich phase diagram involving the competition of small and large black holes. The phase diagram contains a critical line and a critical point similar to the van der Waals-Maxwell liquid-gas transition. As the critical point is approached, we show that the trace anomaly in the plasma phases vanishes signifying the restoration of conformal symmetry in the fluid. We find that the heat capacity and charge susceptibility diverge as $C_V \propto (T-T^c)^{-\alpha}$ and $\chi \propto (T-T^c)^{-\gamma}$ at the critical point with universal critical exponents $\alpha=\gamma=2/3$. Our results suggest a description of the thermodynamics near the critical point in terms of catastrophe theories. In the limit $\mu \to 0$ we compare our results with lattice results for $SU(N_c)$ Yang-Mills theories.

中文翻译：

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爱因斯坦-麦克斯韦-扩张全息在有限温度和密度下的临界性

我们研究了渐近 AdS 的爱因斯坦-麦克斯韦-狄拉顿 (EMD) 方程的一致带电黑洞解。解决方案是在有限温度和密度下非共形等离子体相的重力对偶。对于膨胀，我们采用二次 ansatz 导致在零温度和密度下线性限制。我们考虑化学势固定的正则系综，并找到一个包含大小黑洞竞争的丰富相图。相图包含一条临界线和一个临界点，类似于范德华-麦克斯韦液-气转变。随着临界点的接近，我们表明等离子体相中的痕量异常消失，这意味着流体中的共形对称性恢复。我们发现热容量和电荷敏感性在临界点发散为 $C_V \propto (TT^c)^{-\alpha}$ 和 $\chi \propto (TT^c)^{-\gamma}$通用临界指数 $\alpha=\gamma=2/3$。我们的结果表明，根据灾难理论，可以对临界点附近的热力学进行描述。在极限 $\mu \to 0$ 中，我们将我们的结果与 $SU(N_c)$ Yang-Mills 理论的晶格结果进行比较。