Energy landscapes of spin glasses on the dice lattice

Our study focuses on the potential energy landscapes of three spin models consisting of 36 spins on a dice lattice. The models differ based on the range of interactions between the spins, these are {±1}, {±1,±2}, and {±1,±2,±3}. Due to the discrete nature of these interactions, they form extended minimum energy structures, which we classify into four types: regular minima, type-1, type-2, and type-3 dales. Augmented disconnectivity graphs are used to distinguish these types by color visually. A bar chart illustrates their sizes at each energy. The overall shape of the disconnectivity graphs is dominated by palm leaf structures. Further analysis of the minima structures reveals that in the ±1 model only regular minima and type-1 dales occur, whereas the ±1,±2 and ±1,±2,±3 models show additionally type-2 and type-3 dales, albeit occurring relatively sparsely and confined to the medium energy range. Compared to other lattices, the sizes of the minima structures are smaller and do not exhibit a distinct trend. The occurrence of multiple funnel structures becomes only dominant in the ±1,±2,±3 model, and is further accompanied by a larger number of minima structures, suggesting that this model would be more difficult to optimize in standard optimization procedures. An investigation into the barrier and transition paths shows that barriers are particularly high for low-energy minima and decrease with increasing energy. The transition paths between individual minima suggest that transition states/plateaus are closer to higher energy minima than to lower ones, and that there is a general trend that the length of the transition path decreases with increasing energy.