Spin Glasses: Criticality and Energy Landscapes

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Springer, Jun 28, 2016 - Science - 221 pages
This thesis addresses the surprising features of zero-temperature statics and dynamics of several spin glass models, including correlations between soft spins that arise spontaneously during avalanches, and the discovery of localized states that involve the presence of two-level systems. It also presents the only detailed historiographical research on the spin glass theory. Despite the extreme simplicity of their definition, spin glasses display a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis the author sheds light on some of these, focusing on both the search for phase transitions under perturbations of Hamiltonians and the zero-temperature properties and responses to external stimuli. After introducing spin glasses and useful concepts on phase transitions and numerics, the results of two massive Monte Carlo campaigns on three-dimensional systems are presented: The first of these examines the de Almeida–Thouless transition, and proposes a new finite-size scaling ansatz, which accelerates the convergence to the thermodynamic limit. The second reconstructs the phase diagram of the Heisenberg spin glass with random exchange anisotropy.
 

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Contents

History Simulations and Phase Transition
3
Part II Criticality
43
2 The Ising Spin Glass in a Field
45
3 Heisenberg Spin Glass with Random Exchange Anisotropy
75
Part III Energy Landscapes
96
4 Energy Landscape of mComponent Spin Glasses
99
5 ZeroTemperature Dynamics
115
6 Soft Modes and Localization in Spin Glasses
139
7 Conclusions
163
Appendix AMonte Carlo on Heisenberg Spin Glasses
169
Appendix BFourReplica Correlators
179
Appendix CTechnical Details on the Creation of Quantiles
195
Appendix DDecomposing Conditional Expectations
199
Appendix EManaging the Errors
205
Appendix FThe Inherent Structures
209
Index
217

Part IV Conclusions and Outlook
161

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About the author (2016)

Marco Baity Jesi achieved his bachelor and master degrees at Sapienza, University of Rome. He had the opportunity to spend one year in Paris, between the École Normale Superieure and Université Pierre et Marie Curie. For his masters thesis, a numerical study of spin glasses, he did a research stay at the Universidad Complutense de Madrid, where he collaborated with Victor Martín Mayor. This positive experience lead to a Ph.D. in cotutorship between Madrid and Rome, with Giorgio Parisi and Victor Martín Mayor as advisors. In this period he took advantage of long research stays at NYU and at Upenn. The results of these stays are partly included in his thesis manuscript. The thesis was defended at the end of the year 2015. Dr. Baity Jesi is currently in Paris, working as a postdoctoral fellow for Giulio Biroli at CEA Saclay.