论文标题
Kardar-Parisi-Zhang通用类（$ d+1 $） - 尺寸
Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
论文作者
论文摘要
在任何基板尺寸$ d $中确定KPZ类的确切指数是统计物理学中最重要的开放问题之一。基于其他生长方程的某些确切指数差异的尺寸变化的行为，我在这里发现KPZ生长指数（与波动的时间缩放有关）由$β_D= \ frac {7} {7} {8d+13} $给出。这些指数与文献中对它们的最准确估计提出了极好的一致性。此外，这里通过对随机介质（DPRM）中定向聚合物的离散增长模型（RG）计算的广泛的蒙特卡洛模拟（RG）计算，在这里证实了它们，最高$ d = 15 $。 DPRM能量概率密度函数的左尾指数提供了上述分析结果的另一个惊人验证。
The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences for other growth equations, I find here that the KPZ growth exponents (related to the temporal scaling of the fluctuations) are given by $β_d = \frac{7}{8d+13}$. These exponents present an excellent agreement with the most accurate estimates for them in the literature. Moreover, they are confirmed here through extensive Monte Carlo simulations of discrete growth models and real space renormalization group (RG) calculations for directed polymers in random media (DPRM), up to $d=15$. The left-tail exponents of the probability density functions for the DPRM energy provide another striking verification of the analytical result above.
