Katzav E, Schwartz M
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Nov;60(5 Pt B):5677-80. doi: 10.1103/physreve.60.5677.
A minor modification of the self-consistent expansion (SCE) for the Kardar-Parisi-Zhang (KPZ) system with uncorrelated noise is used to obtain the exponents in systems where the noise has spatial long-range correlations. For d-dimensional systems with correlations of the form D((-->)r-(-->)r',t-t')=2D(0)/(-->)r-(-->)r'/2 rho-d)delta(t-t'), (rho>0), we find a lower critical dimension d(0)(rho)=2+2 rho, above which a perturbative Edwards-Wilkinson (EW) solution appears. Below the lower critical dimension two solutions exist, each in a different, distinct region of rho. For small rho's the solution of KPZ with uncorrelated noise is recovered. For large rho's a rho-dependent solution is found. The existence of only one solution in each region of rho is not a result of a competition between two solutions but a direct outcome of the SCE equation.
对具有不相关噪声的 Kardar-Parisi-Zhang（KPZ）系统的自洽展开（SCE）进行了微小修改，以获得噪声具有空间长程相关性的系统中的指数。对于具有形式为(D(\vec{r}-\vec{r}',t - t') = 2D(0)/|\vec{r}-\vec{r}'|^{2 + \rho} \delta(t - t'))（(\rho>0)）相关性的(d)维系统，我们发现了一个下临界维度(d_0(\rho)=2 + 2\rho)，高于此维度会出现微扰的 Edwards-Wilkinson（EW）解。在下临界维度以下存在两个解，每个解处于(\rho)的不同、独特区域。对于小(\rho)，恢复了具有不相关噪声的 KPZ 解。对于大(\rho)，找到了一个依赖于(\rho)的解。在(\rho)的每个区域中仅存在一个解，这不是两个解之间竞争的结果，而是 SCE 方程的直接结果。
