This award supports theoretical research and education in the use of state-of-the-art computer simulations. The research complements traditional theoretical and experimental approaches in the study of challenging problems in statistical physics that involve phase transitions. The program of research is diverse in scope, broadly developing methods to study phase transitions in systems that cannot be treated analytically. The methods used include Monte Carlo and Spin Dynamics simulations and these employ sophisticated software packages are being enhanced by the research group. This is part of a significant effort in the ongoing exploration and development and refinement of new large-scale simulation methods.
A diverse set of physical systems are examined with particularly attention to those with relevance to magnetic materials, growing films, polymers, and proteins. Both static and dynamic critical phenomena for systems in equilibrium are examined, and this includes simple non-equilibrium models related to film growth and superionic diffusion (driven diffusive systems). Monte Carlo simulations are used to explore models with coupled magnetic and elastic degrees of freedom, lattice systems with geometric frustration (a physical system with intrinsic local frustration between magnetic spins on a pyrochlore lattice) or competing interactions, and systems with finite geometries and associated boundaries. The resulting behavior, which is fundamentally different than that which is found in the bulk, is a primary motivator of the research. Spin dynamics simulations are also used to explore dynamic phenomena for systems in equilibrium. Nonequilibrium behavior is examined in models related to film growth and superionic diffusion is studied using Monte Carlo and Kinetic Monte Carlo methods. The results are compared with those from theory and experiment. The combination of the discovery and explanation of the phase transition behavior and possible new universality classes together with the anticipated methodological developments forms a coherent activity with substantive intellectual substance.
The effort undertaken has broader impacts with both scientific and educational consequences. There are many analogous phenomena in other fields, and the understanding of those systems will also be enhanced. For example, the problem of protein folding has much in common, e.g. a rough ?energy landscape?, with magnetic models with frustration. Many of the algorithmic implementations and advances have applicability to a wide range of simulations in different areas. In many sub-areas of investigation (including chemistry, biochemistry, and statistics) the improvements in Wang-Landau sampling are broadly applicable. The research provides training of graduate students in a broad range of computer simulation methods and enables them to pursue scientific careers in multiple related fields. The Center for Simulational Physics where this work is carried out has an excellent record of educating graduate students from other institutions as well as those from The University of Georgia. The annual Workshop hosted by the Center continues to provide a forum for exchange of ideas and information.
NONTECHNICAL SUMMARY: This award supports research and education in the use of state-of-the-art computer simulations. The research complements traditional theoretical and experimental approaches in the study of challenging problems in statistical physics that involve phase transitions. The program of research is diverse in scope, broadly developing methods to study phase transitions in systems that cannot be treated analytically. The methods employ sophisticated software packages are being enhanced by the research group. This is part of a significant effort in the ongoing exploration and development and refinement of new large-scale computer simulation methods.
A diverse set of physical systems are examined with particularly attention to those with relevance to magnetic materials, growing films, polymers, and proteins. Both static and dynamic phenomena for systems in equilibrium are examined, and this includes simple non-equilibrium models related to film growth and driven diffusive systems. Computer simulations are used to explore models of systems with finite geometries and associated boundaries. The resulting behavior, which is fundamentally different than that which is found in the bulk, is a primary motivator of the research. The results are compared with those from theory and experiment. The combination of the discovery and explanation of the phase transition behavior and possible new phase transitions together with the anticipated methodological developments forms a coherent activity with substantive intellectual substance.
The effort undertaken has broader impacts with both scientific and educational consequences. There are many analogous phenomena in other fields, and the understanding of those systems will also be enhanced. For example, the problem of protein folding has much in common with magnetic models studied. Many of the advances in computer simulation methods have applicability to a wide range of simulations in different areas. In many sub-areas of investigation (including chemistry, biochemistry, and statistics) the improvements are certainly applicable. The research provides training of graduate students in a broad range of computer simulation methods and enables them to pursue scientific careers in multiple related fields. The Center for Simulational Physics where this work is carried out has an excellent record of educating graduate students from other institutions as well as those from The University of Georgia. The annual Workshop hosted by the Center continues to provide a forum for exchange of ideas and information.
Phase transitions in materials, involving dramatic changes in properties as temperature or applied fields change, are central to many areas of physics, and we evolved an active research program employing sophisticated, novel, computer algorithms to investigate such behavior. Even today’s impressive computers are inadequate to simulate complex models that faithfully represent physical systems; hence, we emphasize simple models that retain essential features of phase transitions. Our research, described (incompletely) below, was featured in 24 Invited Lectures at National and International Conferences and 26 Invited Seminars at universities and research institutes. In the simplest view of magnetism, magnetic moments reside on the sites of a rigid lattice. While useful for theory, this view is unrealistic so we have performed Monte Carlo (stochastic) simulations of distortable nets. By varying the nature of the "springs" connecting the moments, we determined that the growth of magnetic "domains" (regions with aligned moments) changes once the lattice restriction is removed. This contrasts with the prevailing Lifshitz-Slyozov theory of domain growth and emphasizes the value of sophisticated computer simulations. The study of wetting of surfaces by a fluid has a long, controversial history in which the interplay between theory and computer simulations played a valuable role. Theory predicted non-universal critical wetting disagreeing with both Monte Carlo simulations and experiment. New predictions of "non-local correlations" between the surface and interface change theoretical behavior. We performed the first test of these predictions, measuring non-local correlations using Monte Carlo simulations and finding a new, non-local correlation length ξNL. Polymers are long-chain molecules with increasing technological and theoretical importance. Many polymers are modeled by chains of beads connected by springs. The collapse of several "bead-spring homopolymer" versions was observed by others using a powerful method known as Wang-Landau sampling (developed in our group); but to resolve conflicting results we performed careful Wang-Landau simulations of bead-spring homopolymers, including special trial moves to help undo knots. The low energy behavior was extracted using state-of-the-art "frontier sampling" (developed in our group), revealing coil-globule and liquid-"solid" transitions. Certain "magic number" lengths showed unique tetrahedral geometries, and low temperature behavior near the liquid-solid transition is rich in structural transformations. Including chain "stiffness" produced a complete phase diagram. The HP lattice protein model is a minimalistic description whose solution is nonetheless forbidding. Wang-Landau sampling combined with suitable trial moves found both the ground state search and the density of states. Thermodynamic properties and "snapshots" of structures showed two stage folding: first a "coil-globule" transition occurs and then the globule rearranges to form a hydrophobic core. We found NO low temperature specific heat peak seen in a benchmark sequence by another group. Our procedure overcomes the limitations inherent in more tailored and elaborate approaches making it broadly applicable, e.g. to complex biological phenomena. Simple checkerboard-like models have enhanced our understanding of adsorbed gas atoms/molecules on crystalline substrates, but not with competing two-body and three-body terms. We simulated such models using GPUs (graphics processing units). Dramatic finite size effects obscured almost convergent phase boundaries between different phases: Small lattice specific heats showed minima whereas with increasing size eventually maxima appeared, signifying phase transitions. Simulations on a nVidia GeForce GTX285 graphics card were 320 times faster than an IBM p655 processor! Using innovative Monte Carlo sampling with "weathervane" trial moves and high-precision spin dynamics simulations, we showed that "novel" excitations reported for the classical Heisenberg antiferromagnet on the kagome lattice were, in fact, illusory!. When a proper global coordinate transformation was invoked, a simple, single-spin wave dispersion curve is found at temperatures orders of magnitude lower than previously achieved. Intellectual merit Our simulations unveiled phase transition and dynamical behavior of multiple models in statistical physics that were not accessible (or incorrectly understood) by other methods. Other simulations verified previously unsubstantiated theoretical predictions. The polymer and protein models that have entropic entanglements proved particularly challenging, and our algorithms provide the only means to determine their properties. Broader impacts Data produced by computer simulations are meaningful only if these techniques are applied with the same care and sophistication as with modern theory or experiment. Many powerful algorithms that we developed are broadly applicable, and our students/postdocs learn the intricacies of these and other methods, error estimation, and visualization. We sponsor weekly "simulations lunch seminars" and an annual Workshop on Recent Developments in Computer Simulations in Condensed Matter Physics. These allow students to hone presentation skills and form international scientific networks. Three women completed advanced degrees, an undergraduate did independent study, and a youngster who began with us as a 9th grader, is studying physics at Stanford U. We hosted faculty and postdocs from Greece, Brazil, Korea and China, and a Ph.D. student from Thailand (all with their own fellowships), and we provided travel fellowships for five graduate/undergraduate students from other institutions to attend our annual Workshops.
