51 research outputs found
On the quality of random number generators with taps
Recent exact analytical results developed for the random number generators
with taps are reported. These results are applicable to a wide class of
algorithms, including random walks, cluster algorithms, Ising models. Practical
considerations on the improvement of the quality of random numbers are
discussed as well.Comment: Conference on Computational Physics, Granada, Spain, 199
Numerical investigation of logarithmic corrections in two-dimensional spin models
The analysis of correlation function data obtained by Monte Carlo simulations
of the two-dimensional 4-state Potts model, XY model, and self-dual disordered
Ising model at criticality are presented. We study the logarithmic corrections
to the algebraic decay exhibited in these models. A conformal mapping is used
to relate the finite-geometry information to that of the infinite plane.
Extraction of the leading singularity is altered by the expected logarithmic
corrections, and we show numerically that both leading and correction terms are
mutually consistent
Critical amplitude ratios of the Baxter-Wu model
A Monte Carlo simulation study of the critical and off-critical behavior of
the Baxter-Wu model, which belongs to the universality class of the 4-state
Potts model, was performed. We estimate the critical temperature window using
known analytical results for the specific heat and magnetization. This helps us
to extract reliable values of universal combinations of critical amplitudes
with reasonable accuracy. Comparisons with approximate analytical predictions
and other numerical results are discussed.Comment: 13 pages, 13 figure
Test of multiscaling in DLA model using an off-lattice killing-free algorithm
We test the multiscaling issue of DLA clusters using a modified algorithm.
This algorithm eliminates killing the particles at the death circle. Instead,
we return them to the birth circle at a random relative angle taken from the
evaluated distribution. In addition, we use a two-level hierarchical memory
model that allows using large steps in conjunction with an off-lattice
realization of the model. Our algorithm still seems to stay in the framework of
the original DLA model. We present an accurate estimate of the fractal
dimensions based on the data for a hundred clusters with 50 million particles
each. We find that multiscaling cannot be ruled out. We also find that the
fractal dimension is a weak self-averaging quantity. In addition, the fractal
dimension, if calculated using the harmonic measure, is a nonmonotonic function
of the cluster radius. We argue that the controversies in the data
interpretation can be due to the weak self-averaging and the influence of
intrinsic noise.Comment: 8 pages, 9 figure
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