标题： 量子BTZ黑洞的临界现象 显示英文标题

标题： Critical phenomenon of quantum BTZ black holes

摘要： 我们通过将量子回波强度参数$\nu$视为热力学变量，扩展了量子BTZ黑洞的热力学理论。 我们发现了各种新颖的特性。 临界点出现在$\nu_c=1$处，并且一级相变要么发生在低于$\nu<\nu_c$的临界温度以下，要么发生在高于$\nu>\nu_c$的临界温度以上。 通过解析地求解共存曲线，我们分析了相结构并阐明了临界点附近的意外间断性。 临界指数显著不同于平均场理论的结果，并且违反了一条标度律。 我们利用热力学势临界行为的普遍三尺度因子假设对此进行了解释。 最后，我们证明了对于任意小的角动量，只能存在一个稳定的黑洞相，因此不会发生相变。 显示英文摘要

摘要： We extend the thermodynamics of quantum BTZ black holes by treating the quantum backreaction strength parameter $\nu$ as a thermodynamic variable. We find various novel features. The critical point appears at $\nu_c=1$ and a first order transition occurs either below the critical temperature for $\nu<\nu_c$ or above the critical temperature for $\nu>\nu_c$. By solving the coexistence curve analytically, we analyze the phase structures and clarify an unexpected discontinuity around the critical point. The critical exponents are significantly different from the mean field theory results and violate one of the scaling laws. We present an intepretation for this by using a universal three scale factor hypothesis for critical behavior of thermodynamic potential. Finally, we prove that given an arbitrarily small angular momenta, only one stable black hole phase can exist and hence no transition will occur.