1,572 research outputs found
BKT-like transition in the Potts model on an inhomogeneous annealed network
We solve the ferromagnetic q-state Potts model on an inhomogeneous annealed
network which mimics a random recursive graph. We find that this system has the
inverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any , including the values , where the Potts model normally shows
a first order phase transition. We obtain the temperature dependences of the
order parameter, specific heat, and susceptibility demonstrating features
typical for the BKT transition. We show that in the entire normal phase, both
the distribution of a linear response to an applied local field and the
distribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure
Potts Model On Random Trees
We study the Potts model on locally tree-like random graphs of arbitrary
degree distribution. Using a population dynamics algorithm we numerically solve
the problem exactly. We confirm our results with simulations. Comparisons with
a previous approach are made, showing where its assumption of uniform local
fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure
Correlations in interacting systems with a network topology
We study pair correlations in cooperative systems placed on complex networks.
We show that usually in these systems, the correlations between two interacting
objects (e.g., spins), separated by a distance , decay, on average,
faster than . Here is the mean number of the
-th nearest neighbors of a vertex in a network. This behavior, in
particular, leads to a dramatic weakening of correlations between second and
more distant neighbors on networks with fat-tailed degree distributions, which
have a divergent number in the infinite network limit. In this case, only
the pair correlations between the nearest neighbors are observable. We obtain
the pair correlation function of the Ising model on a complex network and also
derive our results in the framework of a phenomenological approach.Comment: 5 page
Theory and design of InGaAsBi mid-infrared semiconductor lasers: type-I quantum wells for emission beyond 3 m on InP substrates
We present a theoretical analysis and optimisation of the properties and
performance of mid-infrared semiconductor lasers based on the dilute bismide
alloy InGaAsBi, grown on conventional (001) InP
substrates. The ability to independently vary the epitaxial strain and emission
wavelength in this quaternary alloy provides significant scope for band
structure engineering. Our calculations demonstrate that structures based on
compressively strained InGaAsBi quantum wells (QWs)
can readily achieve emission wavelengths in the 3 -- 5 m range, and that
these QWs have large type-I band offsets. As such, these structures have the
potential to overcome a number of limitations commonly associated with this
application-rich but technologically challenging wavelength range. By
considering structures having (i) fixed QW thickness and variable strain, and
(ii) fixed strain and variable QW thickness, we quantify key trends in the
properties and performance as functions of the alloy composition, structural
properties, and emission wavelength, and on this basis identify routes towards
the realisation of optimised devices for practical applications. Our analysis
suggests that simple laser structures -- incorporating
InGaAsBi QWs and unstrained ternary
InGaAs barriers -- which are compatible with established
epitaxial growth, provide a route to realising InP-based mid-infrared diode
lasers.Comment: Submitted versio
Series Expansion Calculation of Persistence Exponents
We consider an arbitrary Gaussian Stationary Process X(T) with known
correlator C(T), sampled at discrete times T_n = n \Delta T. The probability
that (n+1) consecutive values of X have the same sign decays as P_n \sim
\exp(-\theta_D T_n). We calculate the discrete persistence exponent \theta_D as
a series expansion in the correlator C(\Delta T) up to 14th order, and
extrapolate to \Delta T = 0 using constrained Pad\'e approximants to obtain the
continuum persistence exponent \theta. For the diffusion equation our results
are in exceptionally good agreement with recent numerical estimates.Comment: 5 pages; 5 page appendix containing series coefficient
Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
We compute exactly the distribution of the occupation time in a discrete {\em
non-Markovian} toy sequence which appears in various physical contexts such as
the diffusion processes and Ising spin glass chains. The non-Markovian property
makes the results nontrivial even for this toy sequence. The distribution is
shown to have non-Gaussian tails characterized by a nontrivial large deviation
function which is computed explicitly. An exact mapping of this sequence to an
Ising spin glass chain via a gauge transformation raises an interesting new
question for a generic finite sized spin glass model: at a given temperature,
what is the distribution (over disorder) of the thermally averaged number of
spins that are aligned to their local fields? We show that this distribution
remains nontrivial even at infinite temperature and can be computed explicitly
in few cases such as in the Sherrington-Kirkpatrick model with Gaussian
disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
The IceCube Neutrino Observatory - Contributions to ICRC 2015 Part II: Atmospheric and Astrophysical Diffuse Neutrino Searches of All Flavors
Papers on atmospheric and astrophysical diffuse neutrino searches of all
flavors submitted to the 34th International Cosmic Ray Conference (ICRC 2015,
The Hague) by the IceCube Collaboration.Comment: 66 pages, 36 figures, Papers submitted to the 34th International
Cosmic Ray Conference, The Hague 2015, v2 has a corrected author lis
Improved limits on dark matter annihilation in the Sun with the 79-string IceCube detector and implications for supersymmetry
We present an improved event-level likelihood formalism for including
neutrino telescope data in global fits to new physics. We derive limits on
spin-dependent dark matter-proton scattering by employing the new formalism in
a re-analysis of data from the 79-string IceCube search for dark matter
annihilation in the Sun, including explicit energy information for each event.
The new analysis excludes a number of models in the weak-scale minimal
supersymmetric standard model (MSSM) for the first time. This work is
accompanied by the public release of the 79-string IceCube data, as well as an
associated computer code for applying the new likelihood to arbitrary dark
matter models.Comment: 24 pages, 8 figs, 1 table. Contact authors: Pat Scott & Matthias
Danninger. Likelihood tool available at http://nulike.hepforge.org. v2: small
updates to address JCAP referee repor
An All-Sky Search for Three Flavors of Neutrinos from Gamma-Ray Bursts with the IceCube Neutrino Observatory
We present the results and methodology of a search for neutrinos produced in
the decay of charged pions created in interactions between protons and
gamma-rays during the prompt emission of 807 gamma-ray bursts (GRBs) over the
entire sky. This three-year search is the first in IceCube for shower-like
Cherenkov light patterns from electron, muon, and tau neutrinos correlated with
GRBs. We detect five low-significance events correlated with five GRBs. These
events are consistent with the background expectation from atmospheric muons
and neutrinos. The results of this search in combination with those of
IceCube's four years of searches for track-like Cherenkov light patterns from
muon neutrinos correlated with Northern-Hemisphere GRBs produce limits that
tightly constrain current models of neutrino and ultra high energy cosmic ray
production in GRB fireballs.Comment: 33 pages, 14 figures; minor changes made to match published version
in the Astrophysical Journal, 2016 June 2
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