| dc.description.abstract | Spin glasses are disordered magnetic systems that have frustration. The most interesting feature of the physical properties of spin glasses is the complex structure of phase space that is caused by the competition between the quenched ferromagnetic and antiferromagnetic interactions of spin pairs. The popularity of spin glasses is two-fold. First of all, the extremely complicated energy landscapes built from the frustration among spin interactions gives spin glasses new properties that have never been seen in other ordered systems. One of these properties is a new transition between the paramagnetic phase and a disordered phase, the spin-glass phase. This new phenomenon triggers scientists' enthusiasm for deeply understanding the physical foundations and mathematical description for disordered systems such as spin glasses. Secondly, because analytical methods can no longer offer enough support for studying disordered systems, scientists use numerical tools like Markov-chain Monte Carlo to simulate the thermodynamics of the systems of interest as well as statistical methods to process big data generated from the simulations. Therefore, the research on such complex systems introduces a new paradigm to statistical physics and also opens a window into an overlapping area between computational physics and information science, which makes an interdisciplinary study necessary and helpful.
I devote my research to this new interdisciplinary area by seeking new connections in both models and algorithms. This dissertation consists of two themes. The first theme is about the research of spin glasses, including a study on the universality of a diluted spin-glass model and the development of algorithms by introducing new tools from artificial intelligence and extending the current algorithms for more general use. I demonstrate that to detect the phase transition in a spin-glass model we can train convolutional neural networks with a different spin-glass model. Then, use the convolutional neural networks to precisely predict the phase transition of the model. I also show that by training the convolutional neural networks with poisoned data, the results can be very unpredictable. Next, I introduce research in modifying the isoenergetic cluster moves for highly connected topologies in spin glasses. The numerical results show that isoenergetic cluster moves can only be effective for graphs with low connectivities due to the relatively small percolation thresholds in topologies with high connectivities and the trade-off between the cluster size and acceptance rate forced by the detailed balance condition. To conclude the first theme, I study the universality of the two dimensional Ising model with bond dilution. This project is inspired by a debate in the grey area that is not covered by Harris criterion: the universality of a two-dimensional Ising model with disorder can not be theoretically explained. The simulation results for the two-dimensional Ising model with bond dilution show that the critical exponent of the correction to the correlation length does not change with disorder, which supports the strong universality scenario. The second theme of this dissertation is the study of the Boolean satisfiability problem through the use of Ising spin form. The Boolean satisfiability problem is the problem of determining if there exists an assignment of Boolean variables that satisfies a given Boolean formula. Considering that there are rarely global algorithms for the Boolean satisfiability problem and that the NP-complete Ising spin glass is written in Boolean variables as well, I use Monte Carlo simulations to find the optimal solutions for the Boolean satisfiability problem by implementing the Metropolis algorithm combined with the Parallel tempering algorithm. The advantage of this method is that the ergodicity of the thermodynamic procedure makes this algorithm global, which can help search for optimal solutions through the entire configuration space. The numerical results show that this physical algorithm has an obvious advantage over the current state-of-art algorithms on a derivative problem, the Boolean maximum satisfiability problem. Finally, I introduce my research on the Boolean satisfiability problem-based membership filter. Since the physical approach has the ability of globally seeking solutions it can help find uncorrelated solutions for the Boolean satisfiability problem-based membership filter, which is the key to improving efficiency for this new filter. Furthermore, I improve the efficiency of the filter by turning the Boolean satisfiability instance into a not-all-equal form to guarantee that the solutions found by our algorithm, Borealis, are uncorrelated. The numerical results show that the efficiency of Boolean satisfiability-based filter can be significantly improved while keeping the false positive rate low. | en |
