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We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster random bit generation than the simple algorithm for the 32-bit case and 6.8 times faster for the 64-bit case. Employing the developed algorithm, we apply the multispin coding technique to one-dimensional bond-directed percolation. The simulations are accelerated by up to a factor of 14 compared with an optimized scalar implementation. The random bit string generation algorithm proposed here is applicable to general Monte Carlo methods.
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicists point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality of the diode
The recent work by Achlioptas, DSouza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several ques
In a recent publication (Phys. Rev E 77, 056705 (2008)),we have presented the stochastic Green function (SGF) algorithm, which has the properties of being general and easy to apply to any lattice Hamiltonian of the form H=V-T, where V is diagonal in
In the paper random-site percolation thresholds for simple cubic lattice with sites neighborhoods containing next-next-next-nearest neighbors (4NN) are evaluated with Monte Carlo simulations. A recently proposed algorithm with low sampling for percol
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented trian