Date of Award
5-2024
Degree Type
Honors College Thesis
Academic Program
Physics BS
Department
Physics and Astronomy
First Advisor
Katja Biswas, Ph.D.
Advisor Department
Physics and Astronomy
Abstract
The topology of the potential energy landscape for a spin-glass arranged on the Kagome lattice is studied by the use of enhanced disconnectivity graphs. Enhanced disconnectivity graphs display location and type of minima structures and the barrier heights between them. Three different models which differ in the range of allowed values for the bond strength are analyzed. The allowed values for bond strength for the three different models are {±1}, {±1, ±2}, and {±1, ±2, ±3}. 100 systems were randomly generated for each model, and enhanced disconnectivity graphs were drawn for each system by using the Hamiltonian of the Ising model to calculate the energy. The ±1 model displays a banyan tree structure with highly degenerate ground states and large minima structures. The ±1, ±2 model and the ±1, ±2, ±3 model show a palm tree structure containing single and double funnels. The ±1, ±2 model is dominated by single funnels and the ±1, ±2, ±3 model is dominated by double funnels. These two models also display minima structures that are much smaller than the ±1 model. The results are further analyzed by plotting distributions and a histogram of the overall characteristics of each the models. The distributions emphasize the difference between the three models in terms of the size of the minima structures, the type of minima structure that is the most prevalent, and the number of energy levels.
Copyright
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Recommended Citation
Richardson, Richard, "Disconnectivity Graphs of Spin Glasses on the Kagome Lattice" (2024). Honors Theses. 960.
https://aquila.usm.edu/honors_theses/960