Computational Studies of Disordered Systems in Statistical Physics

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports research and education in computational materials science with application to modeling of disordered materials. The paradigmatic system that will be investigated is the "spin glass". Spin glasses are magnetic materials that order in a complex fashion due to competing interactions at the microscopic level. Theoretical models of spin glasses incorporate these competing interactions and reproduce many of the complex phenomena seen in these materials. Spin glass models have also found applications in neuroscience and evolutionary biology and turn out to have close connections to difficult optimization problems arising in computer science and industrial engineering. The PI's group will develop and use a powerful new computer algorithm called population annealing to study spin glasses and related models. Population annealing has potential applications in many areas of computational science ranging from chemistry and biology to optimization problems in computer science. The project will involve both graduate students and undergraduate students in computational studies. Students will learn advanced computational methods and modern techniques in statistical physics. TECHNICAL SUMMARY This award supports research and education in computational materials science with applications to disordered systems. The population annealing Monte Carlo algorithm is the primary computational tool that will be developed and used. The main emphasis will be on spin glass models but other systems to be studied include the hard square/hard sphere fluids. Glassy systems present formidable intellectual and computational challenges and have remained controversial for decades. Understanding the low temperature properties of spin glasses is a foundational problem of materials science. The large scale computational approach based on the population annealing algorithm combined with new analysis methods promises to clarify the nature of the low temperature phase of Ising spin glasses and to distinguish between competing theories. Spin glass models are closely related to combinatorial optimization problems and understanding spin glasses thus could shed light on many other hard computational problems. For example, temperature chaos in spin glasses is closely related to the computational difficulty of finding ground states using heuristics such as parallel tempering, population annealing or quantum annealing. Population annealing is a new paradigm for equilibrium simulations in statistical physics. The population annealing algorithm promises to find application in a wide range of fields including chemistry, biology and computer science. It is useful both for simulating thermal equilibrium and as a heuristic for finding solutions for combinatorial optimization problems. It is a massively parallel algorithm well suited to distributed computing and thus may pave the way to solving problems in computational physics on a larger scale than previously possible. Combining population annealing with other algorithmic ideas such as kinetic Monte Carlo will expand the range of effective tools available to computational statistical physics for studying systems with rough free energy landscapes. The project will involve both graduate students and undergraduate students in computational studies. Students will learn advanced computational methods and modern techniques in statistical physics.