1,802 research outputs found
Langevin Simulation of the Chirally Decomposed Sine-Gordon Model
A large class of quantum and statistical field theoretical models,
encompassing relevant condensed matter and non-abelian gauge systems, are
defined in terms of complex actions. As the ordinary Monte-Carlo methods are
useless in dealing with these models, alternative computational strategies have
been proposed along the years. The Langevin technique, in particular, is known
to be frequently plagued with difficulties such as strong numerical
instabilities or subtle ergodic behavior. Regarding the chirally decomposed
version of the sine-Gordon model as a prototypical case for the failure of the
Langevin approach, we devise a truncation prescription in the stochastic
differential equations which yields numerical stability and is assumed not to
spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is
supported by a finite size scaling analysis, whereby a massive phase ending at
a line of critical points is clearly observed for the truncated stochastic
model.Comment: 6 pages, 4 figure
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
An approach to NLO QCD analysis of the semi-inclusive DIS data with modified Jacobi polynomial expansion method
It is proposed the modification of the Jacobi polynomial expansion method
(MJEM) which is based on the application of the truncated moments instead of
the full ones. This allows to reconstruct with a high precision the local quark
helicity distributions even for the narrow accessible for measurement Bjorken
region using as an input only four first moments extracted from the data in
NLO QCD. It is also proposed the variational (extrapolation) procedure allowing
to reconstruct the distributions outside the accessible Bjorken region
using the distributions obtained with MJEM in the accessible region. The
numerical calculations encourage one that the proposed variational
(extrapolation) procedure could be applied to estimate the full first
(especially important) quark moments
Ensemble Inequivalence and the Spin-Glass Transition
We report on the ensemble inequivalence in a many-body spin-glass model with
integer spin. The spin-glass phase transition is of first order for certain
values of the crystal field strength and is dependent whether it was derived in
the microcanonical or the canonical ensemble. In the limit of infinitely
many-body interactions, the model is the integer-spin equivalent of the
random-energy model, and is solved exactly. We also derive the integer-spin
equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure
Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
Three decades of work on the quantum field equations of pure Yang-Mills
theory have distilled two families of solutions in Landau gauge. Both coincide
for high (Euclidean) momentum with known perturbation theory, and both predict
an infrared suppressed transverse gluon propagator, but whereas the solution
known as "scaling" features an infrared power law for the gluon and ghost
propagators, the "massive" solution rather describes the gluon as a vector
boson that features a finite Debye screening mass.
In this work we examine the gauge dependence of these solutions by adopting
stochastic quantization. What we find, in four dimensions and in a rainbow
approximation, is that stochastic quantization supports both solutions in
Landau gauge but the scaling solution abruptly disappears when the parameter
controlling the drift force is separated from zero (soft gauge-fixing),
recovering only the perturbative propagators; the massive solution seems to
survive the extension outside Landau gauge. These results are consistent with
the scaling solution being related to the existence of a Gribov horizon, with
the massive one being more general.
We also examine the effective action in Faddeev-Popov quantization that
generates the rainbow and we find, for a bare vertex approximation, that the
the massive-type solutions minimise the quantum effective action.Comment: 13 pages, 7 figures. Change of title to reflect version accepted for
publicatio
On the Phase Structure of the 3D Edwards Anderson Spin Glass
We characterize numerically the properties of the phase transition of the
three dimensional Ising spin glass with Gaussian couplings and of the low
temperature phase. We compute critical exponents on large lattices. We study in
detail the overlap probability distribution and the equilibrium overlap-overlap
correlation functions. We find a clear agreement with off-equilibrium results
from previous work. These results strongly support the existence of a
continuous spontaneous replica symmetry breaking in three dimensional spin
glasses.Comment: 30 pages and 17 figures. Final version to be published in PR
Collective behaviour without collective order in wild swarms of midges
Collective behaviour is a widespread phenomenon in biology, cutting through a
huge span of scales, from cell colonies up to bird flocks and fish schools. The
most prominent trait of collective behaviour is the emergence of global order:
individuals synchronize their states, giving the stunning impression that the
group behaves as one. In many biological systems, though, it is unclear whether
global order is present. A paradigmatic case is that of insect swarms, whose
erratic movements seem to suggest that group formation is a mere epiphenomenon
of the independent interaction of each individual with an external landmark. In
these cases, whether or not the group behaves truly collectively is debated.
Here, we experimentally study swarms of midges in the field and measure how
much the change of direction of one midge affects that of other individuals. We
discover that, despite the lack of collective order, swarms display very strong
correlations, totally incompatible with models of noninteracting particles. We
find that correlation increases sharply with the swarm's density, indicating
that the interaction between midges is based on a metric perception mechanism.
By means of numerical simulations we demonstrate that such growing correlation
is typical of a system close to an ordering transition. Our findings suggest
that correlation, rather than order, is the true hallmark of collective
behaviour in biological systems.Comment: The original version has been split into two parts. This first part
focuses on order vs. correlation. The second part, about finite-size scaling,
will be included in a separate paper. 15 pages, 6 figures, 1 table, 5 video
Instability of one-step replica-symmetry-broken phase in satisfiability problems
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two
random combinatorial problems: k-XORSAT and k-SAT. We present a general method
for establishing the stability of these solutions with respect to further steps
of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari
and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general
combinatorial problems.
It turns out that 1RSB is always unstable at sufficiently small clauses
density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT
is unstable at zero energy for alpha< alpha_m, with alpha_m\approx 4.153. On
the other hand, the SAT-UNSAT phase transition seems to be correctly described
within 1RSB.Comment: 26 pages, 7 eps figure
Finite-size scaling as a way to probe near-criticality in natural swarms
Collective behaviour in biological systems is often accompanied by strong
correlations. The question has therefore arisen of whether correlation is
amplified by the vicinity to some critical point in the parameters space.
Biological systems, though, are typically quite far from the thermodynamic
limit, so that the value of the control parameter at which correlation and
susceptibility peak depend on size. Hence, a system would need to readjust its
control parameter according to its size in order to be maximally correlated.
This readjustment, though, has never been observed experimentally. By gathering
three-dimensional data on swarms of midges in the field we find that swarms
tune their control parameter and size so as to maintain a scaling behaviour of
the correlation function. As a consequence, correlation length and
susceptibility scale with the system's size and swarms exhibit a near-maximal
degree of correlation at all sizes.Comment: Selected for Viewpoint in Physics; PRL Editor's Suggestio
Griffiths singularities in the two dimensional diluted Ising model
We study numerically the probability distribution of the Yang-Lee zeroes
inside the Griffiths phase for the two dimensional site diluted Ising model and
we check that the shape of this distribution is that predicted in previous
analytical works. By studying the finite size scaling of the averaged smallest
zero at the phase transition we extract, for two values of the dilution, the
anomalous dimension, , which agrees very well with the previous estimated
values.Comment: 11 pages and 4 figures, some minor changes in Fig. 4, available at
http://chimera.roma1.infn.it/index_papers_complex.htm
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