Hansen Alex, Kertész János
Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Phys Rev Lett. 2004 Jul 23;93(4):040601. doi: 10.1103/PhysRevLett.93.040601. Epub 2004 Jul 20.
We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.
我们表明，通过选择随机性的适当分布，对最优路径的搜索将无序介质的各种问题联系起来，比如定向渗流、侵入渗流以及定向和非定向的生成聚合物。我们还引入了一种简单高效的算法，该算法能在(O(N^{(1 + d_f/d)}))步内数值求解(d)维模型，其中(d_f)是路径的分形维数。通过二维的广泛模拟，我们确定了定向聚合物普适类的相边界。出现了一个新的强无序相，其中最优路径是具有参数依赖标度指数的自仿射的。此外，相图在特定的点和线上包含定向和非定向渗流以及定向随机游走模型。
