Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Phase Behavior of Type-II Superconductors with Quenched Point Pinning Disorder: A Phenomenological Proposal

A general phenomenology for phase behaviour in the mixed phase of type-II superconductors with weak point pinning disorder is outlined. We propose that the ``Bragg glass'' phase generically transforms via two separate thermodynamic phase transitions into a disordered liquid on increasing the temperature. The first transition is into a glassy phase, topologically disordered at the largest length scales; current evidence suggests that it lacks the long-ranged phase correlations expected of a ``vortex glass''. This phase has a significant degree of short-ranged translational order, unlike the disordered liquid, but no quasi-long range order, in contrast to the Bragg glass. This glassy phase, which we call a ``multi-domain glass'', is confined to a narrow sliver at intermediate fields, but broadens out both for much larger and much smaller field values. The multi-domain glass may be a ``hexatic glass''; alternatively, its glassy properties may originate in the replica symmetry breaking envisaged in recent theories of the structural glass transition. Estimates for translational correlation lengths in the multi-domain glass indicate that they can be far larger than the interline spacing for weak disorder, suggesting a plausible mechanism by which signals of a two-step transition can be obscured. Calculations of the Bragg glass-multi-domain glass and the multi-domain glass-disordered liquid phase boundaries are presented and compared to experimental data. We argue that these proposals provide a unified picture of the available experimental data on both high-T$_c$ and low-T$_c$ materials, simulations and current theoretical understanding.Comment: 70 pages, 9 postscript figures, modified title and minor changes in published versio

Ancient Kura 2010–2011: The first two seasons of joint field work in the Southern Caucasus

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