Numerical Simulations and Machine Learning Modelling of Magnetic Systems

Tian, Zhongzheng, Physics - Graduate School of Arts and Sciences, University of Virginia
Chern, Gia-Wei, University of Virginia

In this study, we show the behaviors of a Gamma model subjected to an external field. A magnetic field in the high-symmetry direction lifts the macroscopic classical ground state degeneracy of the honeycomb Γ model and induces a long-range magnetic order. An intriguing √3 by √3 magnetic order is selected by magnetic field for the antiferromagnetic interaction. At high fields, the breaking of the ground-state Z6 symmetry is through two Berezinskii-Kosterlitz-Thouless transitions that enclose a critical XY phase.

Additionally, we present  a numerical study of the disordered J1-J2 system modeled for a double perovskite compound. We find a glass transition at zero temperature, and derive corresponding critical exponents. We further conduct a Landau-Lifshitz dynamics study for the system to construct its dynamic structure factor, in which we observe a coexistence of spin-wave like dispersion and low energy level non-coherent excitations.

Moreover, we present a transferable machine learning framework that can be applied to analyze system configurations of arbitrary sizes for a certain kind of physics model. The neural network model can make accurate predictions of extensive parameters such as phase and energy. We show that the neural network used in this research has a limitation, in that the energy prediction results have systematic deviations around the phase transition. We infer that this limitation is related to the locality of these extensive parameters. To describe the limitation, we extract a critical exponent that describes how the scaling collapse of phase prediction accuracy curves over the input focus sizes.

PHD (Doctor of Philosophy)
Gamma Model, machine learning, scalability, frustrated magnets, J1-J2 System, honeycomb lattice, finite size scaling, glass order, deep neural network, Kosterlitz-Thouless transition, order by disorder
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