482 research outputs found
Mean-field glass transition in a model liquid
We investigate the liquid-glass phase transition in a system of point-like
particles interacting via a finite-range attractive potential in D-dimensional
space. The phase transition is driven by an `entropy crisis' where the
available phase space volume collapses dramatically at the transition. We
describe the general strategy underlying the first-principles replica
calculation for this type of transition; its application to our model system
then allows for an analytic description of the liquid-glass phase transition
within a mean-field approximation, provided the parameters are chosen suitably.
We find a transition exhibiting all the features associated with an `entropy
crisis', including the characteristic finite jump of the order parameter at the
transition while the free energy and its first derivative remain continuous.Comment: 12 pages, 6 figure
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
A crossing probability for critical percolation in two dimensions
Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in
their extensive numerical investigations of critical percolation in two
dimensions. Cardy was able to find the exact form of pi_h by treating it as a
correlation function of boundary operators in the Q goes to 1 limit of the Q
state Potts model. We extend his results to find an analogous formula for
pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo
changed
Numerical Results For The 2D Random Bond 3-state Potts Model
We present results of a numerical simulation of the 3-state Potts model with
random bond, in two dimension. In particular, we measure the critical exponent
associated to the magnetization and the specific heat. We also compare these
exponents with recent analytical computations.Comment: 9 pages, latex, 3 Postscript figure
Genus Zero Correlation Functions in c<1 String Theory
We compute N-point correlation functions of pure vertex operator states(DK
states) for minimal models coupled to gravity. We obtain agreement with the
matrix model results on analytically continuing in the numbers of cosmological
constant operators and matter screening operators. We illustrate this for the
cases of the and models.Comment: 11 pages, LaTeX, IMSc--92/35. (revised) minor changes plus one
reference adde
Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder
We investigate the explicit renormalization group for fermionic field
theoretic representation of two-dimensional random bond Ising model with
long-range correlated disorder. We show that a new fixed point appears by
introducing a long-range correlated disorder. Such as the one has been observed
in previous works for the bosonic () description. We have calculated
the correlation length exponent and the anomalous scaling dimension of
fermionic fields at this fixed point. Our results are in agreement with the
extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page
Precision preparation of strings of trapped neutral atoms
We have recently demonstrated the creation of regular strings of neutral
caesium atoms in a standing wave optical dipole trap using optical tweezers [Y.
Miroshnychenko et al., Nature, in press (2006)]. The rearrangement is realized
atom-by-atom, extracting an atom and re-inserting it at the desired position
with sub-micrometer resolution. We describe our experimental setup and present
detailed measurements as well as simple analytical models for the resolution of
the extraction process, for the precision of the insertion, and for heating
processes. We compare two different methods of insertion, one of which permits
the placement of two atoms into one optical micropotential. The theoretical
models largely explain our experimental results and allow us to identify the
main limiting factors for the precision and efficiency of the manipulations.
Strategies for future improvements are discussed.Comment: 25 pages, 18 figure
Nematic-Isotropic Transition with Quenched Disorder
Nematic elastomers do not show the discontinuous, first-order, phase
transition that the Landau-De Gennes mean field theory predicts for a
quadrupolar ordering in 3D. We attribute this behavior to the presence of
network crosslinks, which act as sources of quenched orientational disorder. We
show that the addition of weak random anisotropy results in a singular
renormalization of the Landau-De Gennes expression, adding an energy term
proportional to the inverse quartic power of order parameter Q. This reduces
the first-order discontinuity in Q. For sufficiently high disorder strength the
jump disappears altogether and the phase transition becomes continuous, in some
ways resembling the supercritical transitions in external field.Comment: 12 pages, 4 figures, to be published on PR
Influence of rare regions on magnetic quantum phase transitions
The effects of quenched disorder on the critical properties of itinerant
quantum magnets are considered. Particular attention is paid to locally ordered
rare regions that are formed in the presence of quenched disorder even when the
bulk system is still in the nonmagnetic phase. It is shown that these local
moments or instantons destroy the previously found critical fixed point in the
case of antiferromagnets. In the case of itinerant ferromagnets, the critical
behavior is unaffected by the rare regions due to an effective long-range
interaction between the order parameter fluctuations.Comment: 4 pp., REVTe
Symmetry relation for multifractal spectra at random critical points
Random critical points are generically characterized by multifractal
properties. In the field of Anderson localization, Mirlin, Fyodorov,
Mildenberger and Evers [Phys. Rev. Lett 97, 046803 (2006)] have proposed that
the singularity spectrum of eigenfunctions satisfies the exact
symmetry at any Anderson transition. In the
present paper, we analyse the physical origin of this symmetry in relation with
the Gallavotti-Cohen fluctuation relations of large deviation functions that
are well-known in the field of non-equilibrium dynamics: the multifractal
spectrum of the disordered model corresponds to the large deviation function of
the rescaling exponent along a renormalization trajectory
in the effective time . We conclude that the symmetry discovered on
the specific example of Anderson transitions should actually be satisfied at
many other random critical points after an appropriate translation. For
many-body random phase transitions, where the critical properties are usually
analyzed in terms of the multifractal spectrum and of the moments
exponents X(N) of two-point correlation function [A. Ludwig, Nucl. Phys. B330,
639 (1990)], the symmetry becomes , or equivalently
for the anomalous parts .
We present numerical tests in favor of this symmetry for the 2D random
state Potts model with various .Comment: 15 pages, 3 figures, v2=final versio
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