Enhanced Disconnectivity Graphs of the ±1 and ±1, ±2 Spin Glasses

Abstract

The energy landscapes of the ±1 and ±1, ±2 small‐spin glasses are studied in the form of enhanced disconnectivity graphs. This new way of displaying disconnectivity graphs incorporates the merging of minima energy states of equal energy which are connected via zero‐energy spin flips. These states form connected structures on the energy landscape, which we distinguish into four basic types. The types are indicated in the disconnectivity graph by different colors and their respective sizes via a bar chart at the corresponding energy levels. This allows for an easy intuitive access to highly degenerate energy landscapes without losing the main features. Further, these connected minima structures are analyzed in terms of their occurrences, sizes, and distributions for the two models of spin glasses. This gives a deep insight into the energy structure of these systems. Further, the use of the classification of minima reduces the description of ±1 spin models by 93%, and that of ±1, ±2 models by 71% without losing the core information about these systems.