835 research outputs found
Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
We consider the Ising model and the directed walk on two-dimensional layered
lattices and show that the two problems are inherently related: The zero-field
thermodynamical properties of the Ising model are contained in the spectrum of
the transfer matrix of the directed walk. The critical properties of the two
models are connected to the scaling behavior of the eigenvalue spectrum of the
transfer matrix which is studied exactly through renormalization for different
self-similar distributions of the couplings. The models show very rich bulk and
surface critical behaviors with nonuniversal critical exponents,
coupling-dependent anisotropic scaling, first-order surface transition, and
stretched exponential critical correlations. It is shown that all the
nonuniversal critical exponents obtained for the aperiodic Ising models satisfy
scaling relations and can be expressed as functions of varying surface magnetic
exponents.Comment: 22 pages, 8 eps-figures, uses RevTex and epsf, minor correction
Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
The fractal structure of directed percolation clusters, grown at the
percolation threshold inside parabolic-like systems, is studied in two
dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a
dynamical exponent z, the surface shape is a relevant perturbation when k<1/z
and the fractal dimensions of the anisotropic clusters vary continuously with
k. Analytic expressions for these variations are obtained using a blob picture
approach.Comment: 6 pages, Plain TeX file, epsf, 3 postscript-figure
Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation
Two-dimensional directed site percolation is studied in systems directed
along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling
considerations show that the surface is a relevant perturbation to the local
critical behaviour when k<1/z where z=\nu_\parallel/\nu is the dynamical
exponent. The tip-to-bulk order parameter correlation function is calculated in
the mean-field approximation. The tip percolation probability and the fractal
dimensions of critical clusters are obtained through Monte-Carlo simulations.
The tip order parameter has a nonuniversal, C-dependent, scaling dimension in
the marginal case, k=1/z, and displays a stretched exponential behaviour when
the perturbation is relevant. The k-dependence of the fractal dimensions in the
relevant case is in agreement with the results of a blob picture approach.Comment: 13 pages, Plain TeX file, epsf, 6 postscript-figures, minor
correction
Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation
We consider concentric circular defects in the two-dimensional Ising model,
which are distributed according to a generalized Fredholm sequence, i. e. at
exponentially increasing radii. This type of aperiodicity does not change the
bulk critical behaviour but introduces a marginal extended perturbation. The
critical exponent of the local magnetization is obtained through finite-size
scaling, using a corner transfer matrix approach in the extreme anisotropic
limit. It varies continuously with the amplitude of the modulation and is
closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen
model. Through a conformal mapping of the system onto a strip, the gap-exponent
relation is shown to remain valid for such an aperiodic defect.Comment: 12 pages, TeX file + 4 figures, epsf neede
Extended surface disorder in the quantum Ising chain
We consider random extended surface perturbations in the transverse field
Ising model decaying as a power of the distance from the surface towards a pure
bulk system. The decay may be linked either to the evolution of the couplings
or to their probabilities. Using scaling arguments, we develop a
relevance-irrelevance criterion for such perturbations. We study the
probability distribution of the surface magnetization, its average and typical
critical behaviour for marginal and relevant perturbations. According to
analytical results, the surface magnetization follows a log-normal distribution
and both the average and typical critical behaviours are characterized by
power-law singularities with continuously varying exponents in the marginal
case and essential singularities in the relevant case. For enhanced average
local couplings, the transition becomes first order with a nonvanishing
critical surface magnetization. This occurs above a positive threshold value of
the perturbation amplitude in the marginal case.Comment: 15 pages, 10 figures, Plain TeX. J. Phys. A (accepted
Conformal off-diagonal boundary density profiles on a semi-infinite strip
The off-diagonal profile phi(v) associated with a local operator (order
parameter or energy density) close to the boundary of a semi-infinite strip
with width L is obtained at criticality using conformal methods. It involves
the surface exponent x_phi^s and displays a simple universal behaviour which
crosses over from surface finite-size scaling when v/L is held constant to
corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps
Remarks on Duality Transformations and Generalized Stabilizer States
We consider the transformation of Hamilton operators under various sets of
quantum operations acting simultaneously on all adjacent pairs of particles. We
find mappings between Hamilton operators analogous to duality transformations
as well as exact characterizations of ground states employing non-Hermitean
eigenvalue equations and use this to motivate a generalization of the
stabilizer formalism to non-Hermitean operators. The resulting class of states
is larger than that of standard stabilizer states and allows for example for
continuous variation of local entropies rather than the discrete values taken
on stabilizer states and the exact description of certain ground states of
Hamilton operators.Comment: Contribution to Special Issue in Journal of Modern Optics celebrating
the 60th birthday of Peter Knigh
Nonequilibrium phase transition in a driven Potts model with friction
We consider magnetic friction between two systems of -state Potts spins
which are moving along their boundaries with a relative constant velocity .
Due to the interaction between the surface spins there is a permanent energy
flow and the system is in a steady state which is far from equilibrium. The
problem is treated analytically in the limit (in one dimension, as
well as in two dimensions for large- values) and for and finite by
Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase
transitions take place, the properties of which depend on the type of phase
transition in equilibrium. When this latter transition is of first order, a
sequence of second- and first-order nonequilibrium transitions can be observed
when the interaction is varied.Comment: 13 pages, 9 figures, one journal reference adde
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