8 research outputs found
Critical properties of loop percolation models with optimization constraints
We study loop percolation models in two and in three space dimensions, in
which configurations of occupied bonds are forced to form closed loop. We show
that the uncorrelated occupation of elementary plaquettes of the square and the
simple cubic lattice by elementary loops leads to a percolation transition that
is in the same universality class as the conventional bond percolation. In
contrast to this an optimization constraint for the loop configurations, which
then have to minimize a particular generic energy function, leads to a
percolation transition that constitutes a new universality class, for which we
report the critical exponents. Implication for the physics of solid-on-solid
and vortex glass models are discussed.Comment: 8 pages, 8 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 and low-T materials,
simulations and current theoretical understanding.Comment: 70 pages, 9 postscript figures, modified title and minor changes in
published versio