This award supports theoretical and computational research in statistical physics and condensed matter physics organized in three related projects.
1. The PI will develop algorithms for simulating frustrated spin systems and related systems with rough free energy landscapes. The PI aims to improve both the parallel tempering and the population annealing algorithms.
2. The PI will carry out a large-scale computational study of Ising spin glass models. The primary goal of this research is to resolve the controversy over whether, in finite-dimensional systems, spin glass ordering occurs in the simple way as proposed in the droplet picture with only two thermodynamically pure states or through the more complex replica symmetry breaking scenario involving a large multiplicity of pure states. In this study, the PI and collaborators will carry out large scale simulations of Ising spin glasses and analyze the statistics of the overlap distribution using new observables that sharply distinguish these scenarios. The problem of packing hard objects will also be studied using both parallel tempering and population annealing.
3. The last area involves the application of the theory of parallel computational complexity to problems in statistical physics. The notion of P-completeness in parallel computational complexity theory will be extended to sampling problems and applied to prove that growth models such as diffusion limited aggregation are inherently sequential. This work extends and builds on early results that show that diffusion limited aggregation and other processes in statistical physics are P-complete.
This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics.
NON-TECHNICAL SUMMARY This award supports theoretical research and education in statistical and condensed matter physics. The research consists of several related projects that involve computation and concepts that cross disciplinary boundaries.
The PI aims to develop computer algorithms that can overcome the computational challenges of materials that exhibit frustration or barriers to finding the true solution among many possibilities, such as the folded structure of a protein. This general class of problems is important not only in the physical sciences but also in computer science and engineering where they are called combinatorial optimization problems. Spin glasses provide an example of frustration. They are magnetic materials with random interactions between the atomic scale magnetic constituents in these materials often referred to as spins. The random interactions lead to "frustration" spins receive conflicting signals from different neighbors as to which way they should orient themselves. Due to frustration spin glasses take a very long time to reach equilibrium. This is also true for computer simulations of models of spin glasses; they require very long computation times. The PI aims to develop computer algorithms that can overcome the challenges of simulating frustrated systems. The algorithms will then be used to carry out a large scale computational study of spin glasses that will help to resolve a long-standing and fundamental controversy in the theory of disordered materials. The PI will be able to carry out more extensive simulations for lower temperatures than has been possible up to now, and utilize new techniques that can more sharply distinguish between the existence of many equilibrium states or a single pair of states.
The PI also seeks to understand whether computational difficulty of simulations of materials systems on computers with processors that can work in parallel has a fundamental connection to the physical system. The PI will study diffusion limited aggregation, a growth process that describes, for example, mineral deposition and snowflake growth, and creates complex patterns. The question is whether patterns that arise from this process can be generated rapidly by a parallel computer or whether the pattern formation process itself is fundamentally sequential one and not parallelizable. These results may guide the understanding of whether parallelization on a computer will lead to higher performance for a particular problem, and a new way to measure the inherent complexity of a material or other physical system.
This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics.
