14,871 research outputs found
Non Mean-Field Quantum Critical Points from Holography
We construct a class of quantum critical points with non-mean-field critical
exponents via holography. Our approach is phenomenological. Beginning with the
D3/D5 system at nonzero density and magnetic field which has a chiral phase
transition, we simulate the addition of a third control parameter. We then
identify a line of quantum critical points in the phase diagram of this theory,
provided that the simulated control parameter has dimension less than two. This
line smoothly interpolates between a second-order transition with mean-field
exponents at zero magnetic field to a holographic
Berezinskii-Kosterlitz-Thouless transition at larger magnetic fields. The
critical exponents of these transitions only depend upon the parameters of an
emergent infrared theory. Moreover, the non-mean-field scaling is destroyed at
any nonzero temperature. We discuss how generic these transitions are.Comment: 15 pages, 7 figures, v2: Added reference
Onset of criticality and transport in a driven diffusive system
We study transport properties in a slowly driven diffusive system where the
transport is externally controlled by a parameter . Three types of behavior
are found: For the system is not conducting at all. For intermediate
a finite fraction of the external excitations propagate through the system.
Third, in the regime the system becomes completely conducting. For all
the system exhibits self-organized critical behavior. In the middle of
this regime, at , the system undergoes a continuous phase transition
described by critical exponents.Comment: 4 latex/revtex pages; 4 figure
Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature
We investigate systems of nature where the common physical processes
diffusion and fragmentation compete. We derive a rate equation for the size
distribution of fragments. The equation leads to a third order differential
equation which we solve exactly in terms of Bessel functions. The stationary
state is a universal Bessel distribution described by one parameter, which fits
perfectly experimental data from two very different system of nature, namely,
the distribution of ice crystal sizes from the Greenland ice sheet and the
length distribution of alpha-helices in proteins.Comment: 4 pages, 3 figures, (minor changes
The Tangled Nature model as an evolving quasi-species model
We show that the Tangled Nature model can be interpreted as a general
formulation of the quasi-species model by Eigen et al. in a frequency dependent
fitness landscape. We present a detailed theoretical derivation of the mutation
threshold, consistent with the simulation results, that provides a valuable
insight into how the microscopic dynamics of the model determine the observed
macroscopic phenomena published previously. The dynamics of the Tangled Nature
model is defined on the microevolutionary time scale via reproduction, with
heredity, variation, and natural selection. Each organism reproduces with a
rate that is linked to the individuals' genetic sequence and depends on the
composition of the population in genotype space. Thus the microevolutionary
dynamics of the fitness landscape is regulated by, and regulates, the evolution
of the species by means of the mutual interactions. At low mutation rate, the
macro evolutionary pattern mimics the fossil data: periods of stasis, where the
population is concentrated in a network of coexisting species, is interrupted
by bursts of activity. As the mutation rate increases, the duration and the
frequency of bursts increases. Eventually, when the mutation rate reaches a
certain threshold, the population is spread evenly throughout the genotype
space showing that natural selection only leads to multiple distinct species if
adaptation is allowed time to cause fixation.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure
Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions
A monomer-dimer reaction lattice model with lateral repulsion among the same
species is studied using a mean-field analysis and Monte Carlo simulations. For
weak repulsions, the model exhibits a first-order irreversible phase transition
between two absorbing states saturated by each different species. Increasing
the repulsion, a reactive stationary state appears in addition to the saturated
states. The irreversible phase transitions from the reactive phase to any of
the saturated states are continuous and belong to the directed percolation
universality class. However, a different critical behavior is found at the
point where the directed percolation phase boundaries meet. The values of the
critical exponents calculated at the bicritical point are in good agreement
with the exponents corresponding to the parity-conserving universality class.
Since the adsorption-reaction processes does not lead to a non-trivial local
parity-conserving dynamics, this result confirms that the twofold symmetry
between absorbing states plays a relevant role in determining the universality
class. The value of the exponent , which characterizes the
fluctuations of an interface at the bicritical point, supports the
Bassler-Brown's conjecture which states that this is a new exponent in the
parity-conserving universality class.Comment: 19 pages, 22 figures, to be published in Phys. Rev
Reentrant phase diagram of branching annihilating random walks with one and two offsprings
We investigate the phase diagram of branching annihilating random walks with
one and two offsprings in one dimension. A walker can hop to a nearest neighbor
site or branch with one or two offsprings with relative ratio. Two walkers
annihilate immediately when they meet. In general, this model exhibits a
continuous phase transition from an active state into the absorbing state
(vacuum) at a finite hopping probability. We map out the phase diagram by Monte
Carlo simulations which shows a reentrant phase transition from vacuum to an
active state and finally into vacuum again as the relative rate of the
two-offspring branching process increases. This reentrant property apparently
contradicts the conventional wisdom that increasing the number of offsprings
will tend to make the system more active. We show that the reentrant property
is due to the static reflection symmetry of two-offspring branching processes
and the conventional wisdom is recovered when the dynamic reflection symmetry
is introduced instead of the static one.Comment: 14 pages, Revtex, 4 figures (one PS figure file upon request)
(submitted to Phy. Rev. E
Effects of Noise in a Cortical Neural Model
Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made
long-term observations of spontaneous activity of in-vitro cortical networks,
which differ from predictions of current models in many features. In this paper
we generalize the EI cortical model introduced in a previous paper (S.Scarpetta
et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing
effects of noise on the spontaneous activity of the nonlinear system, in order
to account for the experimental results of Segev et al.. Analytically we can
distinguish different regimes of activity, depending from the model parameters.
Using analytical results as a guide line, we perform simulations of the
nonlinear stochastic model in two different regimes, B and C. The Power
Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI)
distributions are computed, and compared with experimental results. In regime B
the network shows stochastic resonance phenomena and noise induces aperiodic
collective synchronous oscillations that mimic experimental observations at 0.5
mM Ca concentration. In regime C the model shows spontaneous synchronous
periodic activity that mimic activity observed at 1 mM Ca concentration and the
PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments
at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function
effects) the PSD shows a broad band peak at low frequency. This feature,
observed experimentally, does not find explanation in the previous models.
Besides we identify parametric changes (namely increase of noise or decreasing
of excitatory connections) that reproduces the fading of periodicity found
experimentally at long times, and we identify a way to discriminate between
those two possible effects measuring experimentally the low frequency PSD.Comment: 25 pages, 10 figures, to appear in Phys. Rev.
Branching annihilating random walks with parity conservation on a square lattice
Using Monte Carlo simulations we have studied the transition from an "active"
steady state to an absorbing "inactive" state for two versions of the branching
annihilating random walks with parity conservation on a square lattice. In the
first model the randomly walking particles annihilate when they meet and the
branching process creates two additional particles; in the second case we
distinguish particles and antiparticles created and annihilated in pairs. Quite
distinct critical behavior is found in the two cases, raising the question of
what determines universality in this kind of systems.Comment: 4 pages, 4 EPS figures include
Universal macroscopic background formation in surface super-roughening
We study a class of super-rough growth models whose structure factor
satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic
background spontaneously develops in the local surface profile, which dominates
the scaling of the local surface width and the height-difference. The shape of
the macroscopic background takes a form of a finite-order polynomial whose
order is decided from the value of the global roughness exponent. Once the
macroscopic background is subtracted, the width of the resulting local surface
profile satisfies the Family-Vicsek scaling. We show that this feature is
universal to all super-rough growth models, and we also discuss the difference
between the macroscopic background formation and the pattern formation in other
models.Comment: 5 pages, LaTex, 1 figure, minor correction
Current-voltage characteristics of the two-dimensional XY model with Monte Carlo dynamics
Current-voltage characteristics and the linear resistance of the
two-dimensional XY model with and without external uniform current driving are
studied by Monte Carlo simulations. We apply the standard finite-size scaling
analysis to get the dynamic critical exponent at various temperatures. From
the comparison with the resistively-shunted junction dynamics, it is concluded
that is universal in the sense that it does not depend on details of
dynamics. This comparison also leads to the quantification of the time in the
Monte Carlo dynamic simulation.Comment: 5 pages in two columns including 5 figures, to appear in PR
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