53 research outputs found
Finite size corrections to disordered systems on Erd\"{o}s-R\'enyi random graphs
We study the finite size corrections to the free energy density in disorder
spin systems on sparse random graphs, using both replica theory and cavity
method. We derive an analytical expressions for the corrections in the
replica symmetric phase as a linear combination of the free energies of open
and closed chains. We perform a numerical check of the formulae on the Random
Field Ising Model at zero temperature, by computing finite size corrections to
the ground state energy density.Comment: Submitted to PR
A New Phenomenology for the Disordered Mixed Phase
A universal phase diagram for type-II superconductors with weak point pinning
disorder is proposed. In this phase diagram, two thermodynamic phase
transitions generically separate a ``Bragg glass'' from the disordered liquid.
Translational correlations in the intervening ``multi-domain glass'' phase are
argued to exhibit a significant degree of short-range order. This phase diagram
differs significantly from the currently accepted one but provides a more
accurate description of experimental data on high and low-T materials,
simulations and current theoretical understanding.Comment: 15 pages including 2 postscript figures, minor changes in published
versio
Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type II Superconductors
A description of a dislocation-free elastic glass phase in terms of domain
walls is developed and used as the basis of a renormalization group analysis of
the energetics of dislocation loops added to the system. It is found that even
after optimizing over possible paths of large dislocation loops, their energy
is still very likely to be positive when the dislocation core energy is large.
This implies the existence of an equilibrium elastic glass phase in three
dimensional random field X-Y magnets, and a dislocation free,
bond-orientationally ordered ``Bragg glass'' phase of vortices in dirty Type II
superconductors.Comment: 12 pages, Revtex, no figures, submitted to Phys Rev Letter
The 3-d Random Field Ising Model at zero temperature
We study numerically the zero temperature Random Field Ising Model on cubic
lattices of various linear sizes in three dimensions. For each random field
configuration we vary the ferromagnetic coupling strength . We find that in
the infinite volume limit the magnetization is discontinuous in . The energy
and its first derivative are continuous. The approch to the thermodynamic
limit is slow, behaving like with for the gaussian
distribution of the random field. We also study the bimodal distribution , and we find similar results for the magnetization but with a
different value of the exponent . This raises the question of the
validity of universality for the random field problem.Comment: 8 pages, 3 PostScript Figure
A cluster Monte Carlo algorithm with a conserved order parameter
We propose a cluster simulation algorithm for statistical ensembles with
fixed order parameter. We use the tethered ensemble, which features Helmholtz's
effective potential rather than Gibbs's free energy, and in which canonical
averages are recovered with arbitrary accuracy. For the D = 2,3 Ising model our
method's critical slowing down is comparable to that of canonical cluster
algorithms. Yet, we can do more than merely reproduce canonical values. As an
example, we obtain a competitive value for the 3D Ising anomalous dimension
from the maxima of the effective potential.Comment: 4 pages, 2 color figures. Minor improvements and update of table
Glassy Motion of Elastic Manifolds
We discuss the low-temperature dynamics of an elastic manifold driven through
a random medium. For driving forces well below the depinning force, the
medium advances via thermally activated hops over the energy barriers
separating favorable metastable states. We show that the distribution of
waiting times for these hopping processes scales as a power-law. This power-law
distribution naturally yields a nonlinear glassy response for the driven
medium, .Comment: 4pages, revte
Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium
We have performed numerical simulation of a 3-dimensional elastic medium,
with scalar displacements, subject to quenched disorder. We applied an
efficient combinatorial optimization algorithm to generate exact ground states
for an interface representation. Our results indicate that this Bragg glass is
characterized by power law divergences in the structure factor . We have found numerically consistent values of the coefficient for
two lattice discretizations of the medium, supporting universality for in
the isotropic systems considered here. We also examine the response of the
ground state to the change in boundary conditions that corresponds to
introducing a single dislocation loop encircling the system. Our results
indicate that the domain walls formed by this change are highly convoluted,
with a fractal dimension . We also discuss the implications of the
domain wall energetics for the stability of the Bragg glass phase. As in other
disordered systems, perturbations of relative strength introduce a new
length scale beyond which the perturbed ground
state becomes uncorrelated with the reference (unperturbed) ground state. We
have performed scaling analysis of the response of the ground state to the
perturbations and obtain . This value is consistent with the
scaling relation , where characterizes the
scaling of the energy fluctuations of low energy excitations.Comment: 20 pages, 13 figure
Mott Transition vs Multicritical Phenomenon of Superconductivity and Antiferromagnetism -- Application to -(BEDT-TTF)X --
Interplay between the Mott transition and the multicritical phenomenon of
d-wave superconductivity (SC) and antiferromagnetism (AF) is studied
theoretically. We describe the Mott transition, which is analogous to a
liquid-gas phase transition, in terms of an Ising-type order parameter .
We reveal possible mean-field phase diagrams produced by this interplay.
Renormalization group analysis up to one-loop order gives flows of coupling
constants, which in most cases lead to fluctuation-induced first-order phase
transitions even when the SO(5) symmetry exists betwen the SC and AF. Behaviors
of various physical quantities around the Mott critical point are predicted.
Experiments in -(BEDT-TTF)X are discussed from this viewpoint.Comment: 4 pages, 9 figures, to appear in J. Phys. Soc. Jp
Phase Transitions in the Two-Dimensional XY Model with Random Phases: a Monte Carlo Study
We study the two-dimensional XY model with quenched random phases by Monte
Carlo simulation and finite-size scaling analysis. We determine the phase
diagram of the model and study its critical behavior as a function of disorder
and temperature. If the strength of the randomness is less than a critical
value, , the system has a Kosterlitz-Thouless (KT) phase transition
from the paramagnetic phase to a state with quasi-long-range order. Our data
suggest that the latter exists down to T=0 in contradiction with theories that
predict the appearance of a low-temperature reentrant phase. At the critical
disorder and for there is no
quasi-ordered phase. At zero temperature there is a phase transition between
two different glassy states at . The functional dependence of the
correlation length on suggests that this transition corresponds to the
disorder-driven unbinding of vortex pairs.Comment: LaTex file and 18 figure
Computational Complexity of Determining the Barriers to Interface Motion in Random Systems
The low-temperature driven or thermally activated motion of several condensed
matter systems is often modeled by the dynamics of interfaces (co-dimension-1
elastic manifolds) subject to a random potential. Two characteristic
quantitative features of the energy landscape of such a many-degree-of-freedom
system are the ground-state energy and the magnitude of the energy barriers
between given configurations. While the numerical determination of the former
can be accomplished in time polynomial in the system size, it is shown here
that the problem of determining the latter quantity is NP-complete. Exact
computation of barriers is therefore (almost certainly) much more difficult
than determining the exact ground states of interfaces.Comment: 8 pages, figures included, to appear in Phys. Rev.
- …