839 research outputs found
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
Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems
We investigate the influence of aperiodic perturbations on the critical
behaviour at a second order phase transition. The bond and site problems are
compared for layered systems and aperiodic sequences generated through
substitution. In the bond problem, the interactions between the layers are
distributed according to an aperiodic sequence whereas in the site problem, the
layers themselves follow the sequence. A relevance-irrelevance criterion
introduced by Luck for the bond problem is extended to discuss the site
problem. It involves a wandering exponent for pairs, which can be larger than
the one considered before in the bond problem. The surface magnetization of the
layered two-dimensional Ising model is obtained, in the extreme anisotropic
limit, for the period-doubling and Thue-Morse sequences.Comment: 19 pages, Plain TeX, IOP macros + epsf, 6 postscript figures, minor
correction
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
Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
The universality class, even the order of the transition, of the
two-dimensional Ising model depends on the range and the symmetry of the
interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the
critical temperature is generally the same due to self-duality. Here we
consider a sudden change in the form of the interaction and study the
nonequilibrium critical dynamical properties of the nearest-neighbor model. The
relaxation of the magnetization and the decay of the autocorrelation function
are found to display a power law behavior with characteristic exponents that
depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.
Quenched bond dilution in two-dimensional Potts models
We report a numerical study of the bond-diluted 2-dimensional Potts model
using transfer matrix calculations. For different numbers of states per spin,
we show that the critical exponents at the random fixed point are the same as
in self-dual random-bond cases. In addition, we determine the multifractal
spectrum associated with the scaling dimensions of the moments of the spin-spin
correlation function in the cylinder geometry. We show that the behaviour is
fully compatible with the one observed in the random bond case, confirming the
general picture according to which a unique fixed point describes the critical
properties of different classes of disorder: dilution, self-dual binary
random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure
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
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