1,559 research outputs found
Critical Exponents near a Random Fractal Boundary
The critical behaviour of correlation functions near a boundary is modified
from that in the bulk. When the boundary is smooth this is known to be
characterised by the surface scaling dimension \xt. We consider the case when
the boundary is a random fractal, specifically a self-avoiding walk or the
frontier of a Brownian walk, in two dimensions, and show that the boundary
scaling behaviour of the correlation function is characterised by a set of
multifractal boundary exponents, given exactly by conformal invariance
arguments to be \lambda_n = 1/48 (\sqrt{1+24n\xt}+11)(\sqrt{1+24n\xt}-1).
This result may be interpreted in terms of a scale-dependent distribution of
opening angles of the fractal boundary: on short distance scales these
are sharply peaked around . Similar arguments give the
multifractal exponents for the case of coupling to a quenched random bulk
geometry.Comment: 13 pages. Comments on relation to results in quenched random bulk
added, and on relation to other recent work. Typos correcte
Time-dependence of correlation functions following a quantum quench
We show that the time-dependence of correlation functions in an extended
quantum system in d dimensions, which is prepared in the ground state of some
hamiltonian and then evolves without dissipation according to some other
hamiltonian, may be extracted using methods of boundary critical phenomena in
d+1 dimensions. For d=1 particularly powerful results are available using
conformal field theory. These are checked against those available from solvable
models. They may be explained in terms of a picture, valid more generally,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate classically through the system.Comment: 4+ pages, Corrected Typo
Holographic Entropy on the Brane in de Sitter Schwarzschild Space
The relationship between the entropy of de Sitter (dS) Schwarzschild space
and that of the CFT, which lives on the brane, is discussed by using
Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The
cosmological constant appears on the brane with time-like metric in dS
Schwarzschild background. On the other hand, in case of the brane with
space-like metric in dS Schwarzschild background, the cosmological constant of
the brane does not appear because we can choose brane tension to cancel it. We
show that when the brane crosses the horizon of dS Schwarzschild black hole,
both for time-like and space-like cases, the entropy of the CFT exactly agrees
with the black hole entropy of 5-dimensional AdS Schwarzschild background as it
happens in the AdS/CFT correspondence.Comment: 8 pages, LaTeX, Referneces adde
Critical behaviour in parabolic geometries
We study two-dimensional systems with boundary curves described by power
laws. Using conformal mappings we obtain the correlations at the bulk critical
point. Three different classes of behaviour are found and explained by scaling
arguments which also apply to higher dimensions. For an Ising system of
parabolic shape the behaviour of the order at the tip is also found.Comment: Old paper, for archiving. 6 pages, 1 figure, epsf, IOP macr
A supersymmetric multicritical point in a model of lattice fermions
We study a model of spinless fermions with infinite nearest-neighbor
repulsion on the square ladder which has microscopic supersymmetry. It has been
conjectured that in the continuum the model is described by the superconformal
minimal model with central charge c=3/2. Thus far it has not been possible to
confirm this conjecture due to strong finite-size corrections in numerical
data. We trace the origin of these corrections to the presence of unusual
marginal operators that break Lorentz invariance, but preserve part of the
supersymmetry. By relying mostly on entanglement entropy calculations with the
density-matrix renormalization group, we are able to reduce finite-size effects
significantly. This allows us to unambiguously determine the continuum theory
of the model. We also study perturbations of the model and establish that the
supersymmetric model is a multicritical point. Our work underlines the power of
entanglement entropy as a probe of the phases of quantum many-body systems.Comment: 16 pages, 8 figure
Fermionic field theory for directed percolation in (1+1) dimensions
We formulate directed percolation in (1+1) dimensions in the language of a
reaction-diffusion process with exclusion taking place in one space dimension.
We map the master equation that describes the dynamics of the system onto a
quantum spin chain problem. From there we build an interacting fermionic field
theory of a new type. We study the resulting theory using renormalization group
techniques. This yields numerical estimates for the critical exponents and
provides a new alternative analytic systematic procedure to study
low-dimensional directed percolation.Comment: 20 pages, 2 figure
Quantum and classical localisation and the Manhattan lattice
We consider a network model, embedded on the Manhattan lattice, of a quantum
localisation problem belonging to symmetry class C. This arises in the context
of quasiparticle dynamics in disordered spin-singlet superconductors which are
invariant under spin rotations but not under time reversal. A mapping exists
between problems belonging to this symmetry class and certain classical random
walks which are self-avoiding and have attractive interactions; we exploit this
equivalence, using a study of the classical random walks to gain information
about the corresponding quantum problem. In a field-theoretic approach, we show
that the interactions may flow to one of two possible strong coupling regimes
separated by a transition: however, using Monte Carlo simulations we show that
the walks are in fact always compact two-dimensional objects with a
well-defined one-dimensional surface, indicating that the corresponding quantum
system is localised.Comment: 11 pages, 8 figure
Long-range epidemic spreading with immunization
We study the phase transition between survival and extinction in an epidemic
process with long-range interactions and immunization. This model can be viewed
as the well-known general epidemic process (GEP) in which nearest-neighbor
interactions are replaced by Levy flights over distances r which are
distributed as P(r) ~ r^(-d-sigma). By extensive numerical simulations we
confirm previous field-theoretical results obtained by Janssen et al. [Eur.
Phys. J. B7, 137 (1999)].Comment: LaTeX, 14 pages, 4 eps figure
Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions
are well-known to exhibit long range magnetic order in dimensions,
but exhibit only quasi long range order, with power law decay of correlations,
in d=1 (for half-integer spin). On the other hand, non-frustrating long range
interactions can induce long range order in d=1. We study Hamiltonians in which
the long range interactions have an adjustable amplitude lambda, as well as an
adjustable power-law , using a combination of quantum Monte Carlo
and analytic methods: spin-wave, large-N non-linear sigma model, and
renormalization group methods. We map out the phase diagram in the lambda-alpha
plane and study the nature of the critical line separating the phases with long
range and quasi long range order. We find that this corresponds to a novel line
of critical points with continuously varying critical exponents and a dynamical
exponent, z<1.Comment: 27 pages, 12 figures. RG flow added. Final version to appear in JSTA
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm
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