全息相变中的临界与多临界Kasner标度
Critical and multicritical Kasner scaling in holographic phase transitions
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中文总结 AI 辅助
该研究探讨全息相变在爱因斯坦-标量黑洞内部Kasner几何上的标度律，推导了不同临界性下Kasner指数的近临界标度关系，通过数值解和解析分析验证了相关预测。
中文摘要 AI 辅助
我们研究全息相变如何将其标度律 imprint 在爱因斯坦-标量黑洞内部的局域Kasner几何上。在固定双迹耦合下，我们推导了第一阶段Kasner指数与史瓦西值偏差的近临界标度：$p_t^{(1)}+\frac{1}{3} \propto O^2 \propto (T_c-T)^{1/r}$，其中$O$表示边界凝聚，$r$对应普通临界性（$r=1$）、三临界性（$r=2$）及更高阶多临界性（$r\geq3$）。超指数标量势生成一系列由标量场反弹分隔的Kasner阶段。我们进一步发现，任何可在相变中连续追踪的后续阶段会继承相同的温度指数，但其系数依赖于阶段。数值解证实了普通与三临界情形下的这些预测。最后，我们解析证明红外不动点的领头无关指数支配低温Kasner标度，并对第一Kasner指数数值验证了所得标度。
英文摘要
We study how holographic phase transitions imprint their scaling laws on the local Kasner geometry inside Einstein-scalar black holes. At fixed double-trace coupling, we derive the near-critical scaling of the deviation of the first-epoch Kasner exponent from the Schwarzschild value: $p_t^{(1)}+\frac{1}{3} \propto O^2 \propto (T_c-T)^{1/r}$, where $O$ denotes the boundary condensate and $r$ labels ordinary criticality ($r=1$), tricriticality ($r=2$), and higher multicriticality ($r\geq3$). A super-exponential scalar potential generates a sequence of Kasner epochs separated by scalar-field bounces. We further find that any later epoch that can be tracked continuously across the transition inherits the same temperature exponent, while its coefficient depends on the epoch. Numerical solutions confirm these predictions for the ordinary and tricritical cases. Finally, we show analytically that the leading irrelevant exponent of the infrared fixed point governs the low-temperature Kasner scaling, and verify the resulting scaling numerically for the first Kasner exponent.
