Energy landscapes of spin models on the Snub Archimedean ( 32, 4, 3, 4) lattice

Abstract

We study the energy landscapes of three spin models, comprised of 36 spins, confined to a Snub Archimedean lattice of type ($3^2$, 4,3,4). Our models differ in the possible range of spin–spin interaction, namely $\{\pm 1\}$, $\{\pm 1,\pm 2\}$, and $\{\pm 1,\pm 2,\pm 3\}$. Characteristic of discrete interactions these spin systems can exhibit extended minimum energy structures which are categorized into four types, namely regular minima, type-1 dales, type-2 dales, and type-3 dales. The different types are distinguished in the disconnectivity graphs via colors and their sizes are indicated for the different energy levels via a bar chart. Each of the models shows distinct features in the structure of the energy landscapes. The $\pm 1$ model only exhibits regular minima, whereas all types are found in the $\pm 1,\pm 2$ and $\pm 1,\pm 2,\pm 3$ models. Their landscapes resemble a palm leaf structure with increasing occurrence of multiple funnels for increasing range of bonds. Further evaluation of these structures reveals that the majority of the minima occupy the medium energy range and that all the structures exhibit high barriers at low energies and low barriers at medium to high energies indicative that low energy traps are more difficult to escape than high energy traps. The length of the transition paths from the minima structures to the transition states allows an investigation into the applicability of Hammond’s postulate to spin systems. The results suggest that for the $\pm 1$ model statistically the configurations of the transition states are closer related to the minima that require less increase in energy than to the minima that require a larger increase in energy. However, due to the presence of flat energy structures, and a larger bond range in the $\pm 1,\pm 2$ and $\pm 1,\pm 2,\pm 3$ models this occurs only up to medium energies.