2,689 research outputs found
Universal crossing probabilities and incipient spanning clusters in directed percolation
Shape-dependent universal crossing probabilities are studied, via Monte Carlo
simulations, for bond and site directed percolation on the square lattice in
the diagonal direction, at the percolation threshold. Since the system is
strongly anisotropic, the shape-dependence enters through the effective aspect
ratio r_eff=cL^z/t, where c is a non-universal constant and z the anisotropy
exponent. A particular attention is paid to the influence of the initial state
on the universal behaviour of the crossing probability. Using anisotropic
finite-size scaling and generalizing a simple argument given by Aizenman for
isotropic percolation, we obtain the behaviour of the probability to find n
incipient spanning clusters on a finite system at time t. The numerical results
are in good agreement with the conjecture.Comment: 8 pages, 12 figures; minor correction
Aperiodic Extended Surface Perturbations in the Ising Model
We study the influence of an aperiodic extended surface perturbation on the
surface critical behaviour of the two-dimensional Ising model in the extreme
anisotropic limit. The perturbation decays as a power of the distance from the
free surface with an oscillating amplitude following some aperiodic sequence.
The asymptotic density is 1/2 so that the mean ampltitude vanishes. The
relevance of the perturbation is discussed by combining scaling arguments of
Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic
perturbations. The relevance-irrelevance criterion involves the decay exponent
of the perturbation, the wandering exponent which governs the fluctuation of
the sequence and the bulk correlation length exponent. Analytical results are
obtained for the surface magnetization which displays a rich variety of
critical behaviours. The results are checked through a numerical
finite-size-scaling study. They show that second-order effects must be taken
into account in the discussion of the relevance-irrelevance criterion. The
scaling behaviours of the first gap and the surface energy are also discussed.Comment: 13 pages, 13 figures, LaTeX2e, EPJ macro
Multiscaling in Ising quantum chains with random Hilhorst-van Leeuwen perturbations
We consider the influence on the surface critical behaviour of a quantum
Ising chain of quenched random surface perturbations decaying as a power of the
distance from the surface (random Hilhorst-van Leeuwen models). We study,
analytically and numerically, the multiscaling behaviour of the surface
magnetization and the surface energy density in the case of marginal
perturbations.Comment: 14 pages, 5 figures, LaTeX2e, epsf, elsar
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