Shapes of tree representations of spin-glass landscapes

Abstract

Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure -- a barrier tree -- the leaves and internal nodes of which represent, respectively, the local minima and the lowest energy saddles connecting those minima. Here we apply several statistics used in the study of phylogenetic trees to barrier trees that result from the energy landscapes of p-spin models. These statistics give information about the shape of these barrier trees, in particular about balance and symmetry. We then ask if they can be used to classify different types of landscapes, compare them with results obtained from random trees, and investigate the structure of subtrees of the barrier trees. We conclude that at least one of the used statistics is capable of distinguishing different types of landscapes, that the barrier trees from p-spin energy landscapes are quite different from random trees, and that subtrees of barrier trees do not reflect the overall tree structure, but their structure is correlated with their ``depth'' in the tree.

arXiv comment14 pages, 6 figures

References in corpus (6)

• Universality Classes for Extreme Value Statistics
• Energy landscapes, supergraphs, and "folding funnels" in spin systems
• Landscape statistics of the low autocorrelated binary string problem
• Fractal geometry of spin-glass models
• Landscape statistics of the p-spin Ising model
• Metastable States in High Order Short-Range Spin Glasses

Cited by in corpus (6)

• Random Walk over Basins of Attraction to Construct Ising Energy Landscapes
• The energy landscape networks of spin-glasses
• Phase transition and landscape statistics of the number partitioning problem
• Intermittent relaxation in hierarchical energy landscapes
• Adding color: Visualization of energy landscapes in spin glasses
• Memory effect and phase transition in a hierarchical trap model for spin glass