Date of Award
5-2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
Dr. Katja Biswas
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Parthapratim Biswas
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Khin Maung Maung
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
Dr. Andrew Sung
Committee Member 4 School
Computing Sciences and Computer Engineering
Committee Member 5
Dr. Rajamohan Kalluru Reddy
Committee Member 5 School
Mathematics and Natural Sciences
Abstract
This dissertation presents a detailed analysis of the potential energy landscapes of spin glass systems defined on Snub Archimedean (32, 4, 3, 4 ) lattices, Dice lattices, Elongated Triangular (33, 42), and Hexagonal Honeycomb (63) Lattices. Each system consists of 36 spins. Three distinct systems were considered based on the range of interaction of the spin-spin couplings: {±1}, {±1,±2}, and {±1,±2,±3}. Energy minima were classified into regular minima, type-1 dales, type-2 dales, and type-3 dales due to the discrete nature of interactions, which can form extended minimum energy structures.
Disconnectivity graphs were used to display the minima distributions, while the bar chart helped to distinguish their size at different energy levels. The overall energy landscape structure in different lattices is dominated by palm leaf structures. The lattices with odd coordination number have only regular minima, whereas the mixed-bond (with both even and odd coordination number) lattices have regular minima and type-1 dales in the {±1}model. This analysis further explains the presence of a local funnel, multiple local funnels, and a multi-ground state funnel, which increases the complexity of the optimization challenge. The Elongated triangular lattice(ETL) has a higher number of multiple funnels and multi-ground state funnels as compared to other lattices in {±1,±2,±3}. Most of the systems exhibit degenerate ground states across all models, arising from frustration and bond disorder. The barrier height analysis shows that barriers at low-energy minima are separated by relatively high barriers, which decrease with increasing energy and converge after mid-energy range. The higher interaction range models have a higher barrier heights at low energy. A pronounced peak of specific heat capacity is found in same temperature for all spin but shifted for each model and no significant effect on finite size effect.
Copyright
© Anil Kumar Katwal, 2026. All rights reserved.
Recommended Citation
Katwal, Anil Kumar, "Energy Landscape of Spin Glass Systems on Lattices" (2026). Dissertations. 2467.
https://aquila.usm.edu/dissertations/2467
Included in
Condensed Matter Physics Commons, Statistical, Nonlinear, and Soft Matter Physics Commons