Energy Landscapes of Spin Glasses on Three Archimedean Lattices

Augmented disconnectivity graphs are used to visualize and analyze the potential energy landscape of spin glasses. The disconnectivity graphs show the energy minima of the systems and the lowest highest barriers connecting the minima. Due to the effects of frustration, these minima can form extended structures on the energy landscape, which are classified into three types. Together with regular minima, they are the type-1, type-2, and type-3 dales. In the disconnectivity graphs, the different types are distinguished via colors, and their sizes are indicated for the different energy levels. This classification provides in-depth insight when analyzing the properties of spin glasses, which I will illustrate with examples of spin glasses on the triangular (3^6), the Kagome (3,6,3,6), and the Snub Archimedean (3^2,4,3,4) lattices. Each of the lattice topologies shows distinct characteristics in the occurrence and size of the minima structures, providing valuable information about the complexity of the systems, their accessibility to optimization procedures, and their implications for kinetic processes. Further, the effects of the lattice topology are compared to the effects of different bond strengths, namely ${\pm1}$, ${\pm1,\pm2}$, and ${\pm1,\pm2,\pm3}$. The ${\pm1}$ models of the triangular and Kagome lattices exhibit a banyan tree structure of the energy landscape, whereas the ${\pm1}$ model of the Snub lattice resembles a palm leaf structure. For larger bond ranges all models resemble palm leaf and palm tree structures with increasing occurrence of multiple funnels at larger bond ranges.