Phases and Dynamics of Disordered Condensed Matter Systems

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0109164MiddletonThis award supports theoretical research, algorithm development, numerical simulations and analyses on a wide range of models for physical systems with quenched disorder. Sample systems modeled using classical degrees of freedom include random magnets, such as spin glasses, type-II superconductors, where magnetic flux is pinned by disorder, and even biologically important polymers, such as proteins and RNA. Optimization algorithms developed over the past few years have broadened the number of model systems with ground state and equilibrium behavior that can be studied with precision. In many cases, exact ground states or partition functions can be found in time polynomial in the system size. The PI will extend the number of models that can be studied using such algorithms and develop new algorithms to generate excitations and to study nonequilibrium behavior. One application will be to determine critical exponents more accurately, for studying scaling pictures for these models. In addition, recent work has directly addressed some of the more subtle, qualitative questions about disordered systems, such as the number of nearly degenerate optima, the nature of the thermodynamic limit, and the nature of large, lowest energy excitations. These questions will be studied for more models, with the goal of unifying the description of disordered models. In addition, the details of thermal activation and equilibration will be studied using new approaches. These will enable the study how memory effects take place in disordered magnets.Collective transport through quenched disorder occurs in a number of physical systems, including solid-on-solid friction, fluid flowing over rough surfaces, moving colloidal crystals in disordered backgrounds, and magnetic flux motion in superconductors. Some types of motion, e.g., overdamped elastic media driven through disorder, are well understood. There are many simulations and experiments for which a general understanding of plastic flow, where particles can slide by each other and the transport is inhomogeneous, is lacking. The PI plans to continue to explore a model for such flow. This model, which interpolates between well understood elastic flow and plastic flow, can be solved exactly at the mean field level. This model will be extended to more realistic applications in finite dimensions, where potentially universal critical behavior, at the transition from hysteretic to non-hysteretic flow, is amenable to experimental study in a number of systems. The PI will extend work on charge transport in arrays of metallic dots, which is a useful model for studying channel-like flow and questions of universality. The research activity supports the training of students in state of the art computational and statistical mechanical methods.%%%This award supports theoretical and computational research, and education on the statistical mechanics and driven dynamics of extended physical systems with quenched disorder. The work encompasses a wide range of physical systems, for example, random magnets, such as spin glasses, type-II superconductors, where magnetic flux is pinned by disorder, and even biologically important polymers, such as proteins and RNA. The research is interdisciplinary, involving algorithmic development that impacts both computer science and computational condensed matter and materials physics, and activities at the interface between statistical physics and computational complexity. Specific research activities lie in two general areas: (1) equilibrium and near equilibrium behavior, including memory effects, in disordered statistical mechanical systems, and (2) models for plastic flow, which are applicable to flux flow in superconductors and to transport in charge density wave materials, and a novel model for charge transport. The thrust of the work is fundamental, intended to discover universal properties of, and physical connections among, diverse disordered systems, as well as, specific physical properties of a large number of models which can be compared with experiments, many of which involve phenomena important to everyday uses of materials.***