Energy landscapes of spin glasses on triangular Archimedean lattices

Enhanced disconnectivity graphs are compared for three different models of spin systems constrained to an Archimedean triangular lattice with periodic boundary conditions. Each spin is connected to six nearest neighbors, and the systems differ in the range of values of their bonds namely {& PLUSMN;1}, {& PLUSMN;1, & PLUSMN;2} and {& PLUSMN;1, & PLUSMN;2, & PLUSMN;3}. The enhanced disconnectivity graphs allow for a larger energy range to be depicted and show a clear difference in their structure for the three models. The {& PLUSMN;1} model exhibits a banyan tree structure dominated by large dales which are almost all at the ground state. The {& PLUSMN;1, & PLUSMN;2} model shows a palm tree structure representative of a single funnel with dales as ground states. Whereas the {& PLUSMN;1, & PLUSMN;2, & PLUSMN;3} model exhibits a double funnel structure. This indicates different accessibility of ground states and can serve as a tool for understanding the difficulties faced by optimization routines and their effectiveness. The disconnectivity graphs are further evaluated concerning the types, sizes, and distributions of the types of minima, giving a detailed insight into the structure of their energy landscape. Overall, while a smaller range of the bonds shows a narrowing range of the energy values, it also leads to a broadening of the connected energy structures.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This article compares enhanced disconnectivity graphs for three different models of spin systems constrained to an Archimedean triangular lattice. The graphs show clear differences in structure for the three models, indicating different accessibility of ground states. The graphs can serve as a tool for understanding the difficulties faced by optimization routines and their effectiveness. Additionally, the graphs provide detailed insight into the structure of the energy landscape.