3,930 research outputs found
Geometric explanation of anomalous finite-size scaling in high dimensions
We give an intuitive geometric explanation for the apparent breakdown of
standard finite-size scaling in systems with periodic boundaries above the
upper critical dimension. The Ising model and self-avoiding walk are simulated
on five-dimensional hypercubic lattices with free and periodic boundary
conditions, by using geometric representations and recently introduced
Markov-chain Monte Carlo algorithms. We show that previously observed anomalous
behaviour for correlation functions, measured on the standard Euclidean scale,
can be removed by defining correlation functions on a scale which correctly
accounts for windings.Comment: 5 pages, 4 figure
High-precision Monte Carlo study of directed percolation in (d+1) dimensions
We present a Monte Carlo study of the bond and site directed (oriented)
percolation models in dimensions on simple-cubic and
body-centered-cubic lattices, with . A dimensionless ratio is
defined, and an analysis of its finite-size scaling produces improved estimates
of percolation thresholds. We also report improved estimates for the standard
critical exponents. In addition, we study the probability distributions of the
number of wet sites and radius of gyration, for .Comment: 11 pages, 21 figure
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