Dynamics of Disordered Non-equilibrium Systems: Hysteresis, Noise, and Domain Wall Dynamics in Systems Ranging from Magnets to Earthquakes

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0072783DahmenThis grant supports theoretical research in condensed matter and materials physics. An increased interest in real materials has brought much attention to disordered systems. Disorder changes the free-energy landscape of a system and can lead to large energy barriers between metastable states, resulting in extremely slow approaches to equilibrium, as seen in many experiments. There has been much progress made recently in the study of distinctly nonequilibrium effects, such as collective response to an external driving force (avalanches) and internal history dependence of the system (hysteresis). This project deals with different effects of disorder on long length-scale behavior in hysteretic systems.On long length-scales, where local fluctuations in the amount of disorder are averaged out, systems driven far from equilibrium can often be usefully described by simple laws, and universal, i.e., detail independent, critical behavior has been detected. Examples range from collective dynamics of advancing domain walls in magnetic tapes to event size distributions of earthquakes. The methods applied include ideas from dynamical systems and chaos, critical phenomena, hydrodynamics and disordered systems theory.Hysteresis loops are often seen in experiments at first-order phase transformations when the systems goes out of equilibrium. They may have a macroscopic jump, roughly as seen in the supercooling of liquids, or they may be smoothly varying, as seen in most magnets. In a recent collaboration with the Sethna group at Cornell, we have studied the non-equilibrium zero-temperature random-field Ising model as a model for hysteretic behavior at first-order transformations. As disorder is added, one finds a transition where the jump in the magnetization (corresponding to an infinite avalanche) decreases to zero. At this transition, the model exhibits power law distributions of noise (avalanches), universal behavior and a diverging length-scale. The effect of adding temperature fluctuations and finite field sweep rate to the system will be studied. Tuning the sweep frequency allows the entire experimetally relevant crossover regime to be studied between the two extreme cases that are found in the literature (far from and close to equilibrium). The results will be used to interpret experiments in magnetic systems and to pursue related questions relevant to industrial applications.%%%This grant supports theoretical research in condensed matter and materials physics. An increased interest in real materials has brought much attention to disordered systems. Disorder changes the free-energy landscape of a system and can lead to large energy barriers between metastable states, resulting in extremely slow approaches to equilibrium, as seen in many experiments. There has been much progress made recently in the study of distinctly nonequilibrium effects, such as collective response to an external driving force (avalanches) and internal history dependence of the system (hysteresis). This project deals with different effects of disorder on long length-scale behavior in hysteretic systems such as magnets.***