|dc.description.abstract||In this thesis, we present two explorations: (1) understanding the mechanism causing reentrant behavior in the rare-earth pyrochlore magnet Er2Sn2O7, and (2) determining if unsupervised machine learning is capable of uncovering quenched gauge symmetries.
(1) Recent heat capacity measurements have been performed on newly-available single crystal samples of Er2Sn2O7 under an applied magnetic field H. For the , , and  field directions, the resulting (H, T) phase diagrams all exhibit reentrant lobes: as a function of H for certain fixed values of T, the system transitions from disordered to ordered and back to disordered. We demonstrate that, broadly speaking, multiphase competition is the origin of this reentrant behavior. In particular, two types of multiphase competition operate in Er2Sn2O7: (i) competition that is induced by the applied field H between ordered states of different symmetry, and (ii) competition present from the zero-field ground state of Er2Sn2O7. Using a combination of classical Monte Carlo simulations, mean-field theory, and classical spin-wave expansions, we show that both types of multiphase competition produce soft spin-wave modes not present in the zero-field ground state. These increase thermal fluctuations and entropically stabilize the ordered phase, thereby producing reentrance. It is argued that dipolar interactions do not change this microscopic mechanism. Implications for other materials are discussed.
(2) A major application of machine learning techniques to condensed matter physics has focused on learning thermodynamic quantities such as order parameters and phase transitions. However, since the simulated models follow physical laws that are mathematical in nature, one may ask if machine learning can provide information about the model itself. We explore this question with the Mattis Ising spin glass (MISG) and Mattis XY gauge glass (MXYGG) models, which can be mapped onto the ferromagnetic Ising and XY models under a gauge transformation. Using the well-established unsupervised Principal Component Analysis (PCA) method, we answer the above question affirmatively. PCA classifies the phases of the MISG and MXYGG models in the same manner as the regular Ising and XY models, indicating it has detected their gauge symmetries. Moreover, PCA provides a quantitative estimate of the gauge transformation that establishes this mapping, despite being provided no information about it. This demonstrates that unsupervised machine learning can provide insights into simulated models themselves. The implications of this idea are discussed.||en