Phase Diagram of Optimal Paths

Details Phase Diagram of Optimal Paths Phase Diagram of Optimal Paths

2004-02-17

arxiv.org/abs/cond-mat/0402430v1

Physics

Condensed Matter

Statistical Mechanics

4 pages RevTeX, 4 figures

Scientific paper

10.1103/PhysRevLett.93.040601

We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in order N^(1+d_f/d) steps where d_f 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 non-directed percolation as well as the directed random walk models at specific points and lines.

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