Phase Diagram of Optimal Paths
arXiv:cond-mat/0402430 · doi:10.1103/PhysRevLett.93.040601
Abstract
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.
arXiv comment4 pages RevTeX, 4 figures
References in corpus (8)
- Nonequilibrium Dynamics of Interfaces and Lines
- Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
- Flow Between Two Sites on a Percolation Cluster
- Optimal Path in Two and Three Dimensions
- Non-universal exponents in interface growth
- Directed Polymer -- Directed Percolation Transition
- Universal properties of shortest paths in isotropically correlated random potentials
- Universality of the Directed Polymer Model
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