Random Walk over Basins of Attraction to Construct Ising Energy Landscapes
arXiv:1104.1215 · doi:10.1103/PhysRevLett.106.180602
Abstract
An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the SK spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.
arXiv comment2 Figures and 1 Table. To be published in Physical Review Letters
References in corpus (12)
- Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
- An efficient, multiple range random walk algorithm to calculate the density of states
- Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
- The Complexity of Ising Spin Glasses
- Energy landscapes, supergraphs, and "folding funnels" in spin systems
- Power-law distributions for the areas of the basins of attraction on a potential energy landscape
- Numerical study of metastable states in Ising spin glasses
- Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
- Shapes of tree representations of spin-glass landscapes
- The energy landscape networks of spin-glasses
- From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses
- Fractal geometry of spin-glass models
Cited by in corpus (6)
- Inferring large graphs using l1-penalized likelihood
- Energy landscape analysis based on the Ising model: Tutorial review
- Energy landscapes of combinatorial optimization in Ising machines
- Mapping Energy Landscapes of Non-Convex Learning Problems
- Adding color: Visualization of energy landscapes in spin glasses
- Building a Telescope to Look Into High-Dimensional Image Spaces