Biased and greedy random walks on two-dimensional lattices with quenched randomness: the "greedy" ant within a disordered environment
arXiv:1308.4269 · doi:10.1103/PhysRevE.88.062101
Abstract
The principle characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here, the disorder allows for negative edge-weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization (ACO) heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter rho that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of rho for different bias strengths B is put under scrutiny. Upon tuning rho, the probability to find such a feasible lattice walk increases from zero to one. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point rho_c, resulting from numerically exact and "static" simulations in terms of the NWP model can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.
arXiv comment14 pages, 7 figures
References in corpus (14)
- Modeling the Searching Behavior of Social Monkeys
- Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
- Fractal dimension of domain walls in two-dimensional Ising spin glasses
- Drift and trapping in biased diffusion on disordered lattices
- Anomalous biased diffusion in networks
- Negative-weight percolation
- A dedicated algorithm for calculating ground states for the triangular random bond Ising model
- Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition
- The upper critical dimension of the negative-weight percolation problem
- Phase transitions in diluted negative-weight percolation models
- Scaling of loop-erased walks in 2 to 4 dimensions
- Mean-field behavior of the negative-weight percolation model on random regular graphs
- Configurational statistics of densely and fully packed loops in the negative-weight percolation model
- Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6