Network of inherent structures in spin glasses: scaling and scale-free distributions

Abstract

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic ``length scale'' grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, for spin glasses based on random graphs, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free tail.

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References in corpus (18)

• Emergence of scaling in random networks
• The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
• Inherent Structure Entropy of Supercooled Liquids
• The network topology of a potential energy landscape: A static scale-free network
• The potential energy landscape of a model glass former: thermodynamics, anharmonicities, and finite size effects
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
• Hopping in a Supercooled Lennard-Jones Liquid: Metabasins, Waiting Time Distribution, and Diffusion
• Self-similar disk packings as model spatial scale-free networks
• Connected Network of Minima as a Model Glass: Long Time Dynamics
• On the dynamics of the glass transition on Bethe lattices
• Transitions between Inherent Structures in Water
• Inherent structures and non-equilibrium dynamics of 1D constrained kinetic models: a comparison study
• The distance between Inherent Structures and the influence of saddles on approaching the mode coupling transition in a simple glass former
• Energy distribution of maxima and minima in a one-dimensional random system
• From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses
• Inherent structures dynamics in glasses: a comparative study
• Real space analysis of inherent structures

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• Partition of Networks into Basins of Attraction
• Complex networks and glassy dynamics: walks in the energy landscape
• Complex systems: features, similarity and connectivity
• Inherent Structures in m-component Spin Glasses
• Distribution of metastable states of Ising spin glasses
• Scattering theory of transport through disordered magnets
• Adding color: Visualization of energy landscapes in spin glasses