Jesi M.B. Spin Glasses: Criticality and Energy Landscapes (Springer Theses)

Springer International Publishing, Switzerland, 2016. — 239 p. — ISBN: 9783319412306This thesis combines theoretical physics with rigorous computational applications to achieve state-of-the art analyses of spin glasses. After a detailed historical introduction of the origin of spin glass theory, the author formulates and solves a series of open problems about the nature of these systems. Among the most noteworthy findings of the research exercise are the following: development of a new finite-size scaling ansatz for the study of the phase transition in a field, which
accelerates convergence towards the thermodynamic limit; identification of the phase diagram for three-dimensional spin glasses with a random anisotropic exchange (this solution, obtained through a massive Monte Carlo campaign, likely represents the first open question on spin glasses to be solved through the use of GPUs); characterization of the effect of the number of spin components on the energy landscape of a spin glass; observation of correlations between soft spins that arise spontaneously during avalanches; and discovery that spin glasses are a nontrivial model exhibiting two-level systems.
These and other scientific results are presented in a clear and understandable format, in order for the reader to appreciate the latest research advancements in the field.An Introduction to Spin Glasses: History, Simulations and Phase Transition
Criticality
The Ising Spin Glass in a Field
Heisenberg Spin Glass with Random Exchange Anisotropy
Energy Landscapes
Energy Landscape of m-Component Spin Glasses
Zero-Temperature Dynamics
Soft Modes and Localization in Spin Glasses
Conclusions and Outlook
Conclusions
Appendixes
Monte Carlo on Heisenberg Spin Glasses
Four-Replica Correlators
Technical Details on the Creation of Quantiles
AppendDecomposing Conditional Expectations
Managing the Errors
The Inherent Structures