景观侵蚀中的标度：具有无限多耦合的模型的重整化群分析
Scaling in erosion of landscapes: Renormalization group analysis of a model with infinitely many couplings
摘要：
将标准场论重整化群应用于R. Pastor-Satorras和D. H. Rothman [Phys. Rev. Lett. 80：4349（1998）; J. Stat.第九十三章：477（1998）]产生了意想不到的结果：只有当模型涉及无穷多个耦合常数时，模型才是可乘法重正化的（即，相应的重整化群方程涉及无穷多个β函数）。尽管如此，单回路反项可以根据进入原始随机方程的某个函数$V(h)$及其关于高度场$h$的导数导出，尽管是封闭形式。它的泰勒展开产生了完整的无限集的单圈重整化常数，β函数和反常尺寸。代替一组固定点，存在可能包含红外吸引区域的固定点的二维表面。如果是这样的话，该模型在红外范围内表现出缩放行为。相应的临界指数通过对曲面上不动点坐标的依赖而具有非普适性，但满足一定的普适精确关系。
英文摘要：
Standard field theoretic renormalization group is applied to the model of landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected results: the model is multiplicatively renormalizable only if it involves infinitely many coupling constants ( i.e., the corresponding renormalization group equations involve infinitely many beta-functions). Despite this fact, the one-loop counterterm can be derived albeit in a closed form in terms of the certain function $V(h)$, entering the original stochastic equation, and its derivatives with respect to the height field $h$. Its Taylor expansion gives rise to the full infinite set of the one-loop renormalization constants, beta-functions and anomalous dimensions. Instead of a set of fixed points, there is a two-dimensional surface of fixed points that is likely to contain infrared attractive region(s). If that is the case, the model exhibits scaling behaviour in the infrared range. The corresponding critical exponents are nonuniversal through the dependence on the coordinates of the fixed point on the surface, but satisfy certain universal exact relations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
