Aspects geometric and random frustration in magnetic

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Frustration in condensed matter physics arises when a system cannot minimize its total energy by minimizing the energy of each pair of interacting degrees of freedom independently from each other. Both uniformly and random frustrated systems are ubiquitous in condensed matter physics. Examples range from magnetic and superconducting system, to biological membranes and proteins. Geometric frustration arises purely from geometrical constraints imposed by the system considered. Random frustration results from the frozen-in (quenched) random disorder that is always present in any real material, and which create randomly competing or "randomly frustrating" interactions. Because geometric and random frustration is so common, it is important to understand on a theoretical footing their effects in real materials. This is the focus of this research proposal. For example, problems to be tackled in this research program include: