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W�X�Y�Z
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14
cosmic structure in self-organized percolation models
Miao Haixing,Zhang Yang,Hou Yonghui
University of Science and Technology of Chian
http://www.paper.edu.cn
Abstract
A study on the large scale structure of the Universe is carried out in the percolation
model commonly used to explain continuous phase transition. Although the critical-state
percolation model previously studied accords qualitatively with the observational result, a
fine-tuning parameter, the propagation probability P = Pc, is required in order to keep
the system in the critical state. By analysising the formation process of galaxies, it is
noted that the self-organized percolation model without the fine-tuning takes into account
of the back-reaction from the enveroment of the actual structure formation. Based on
this self-organized percolation model, we have performed numerical simulations on the
simple cubic lattice in 3-dim space, obtained the numerical samples for the spatial galaxy
distribution, and calculated the two-point correlation function ξ(r), which is quite similar
to that from the percolation model in critical state. We have also given the corresponding
power spectrum P (k), which behaves ∼ k−2.1 on large scale, and ∼ k−2.6 on small scale,
also agreeing qualitatively with the observations. Goemetrically the spatial distribution of
galaxies is more adequately described by the off-lattice model instead of the simple cubic
lattice model. We have also performed simulations on the off-lattice, and the resulting
ξ(r) and P (k) are similar to the lattice case. The major difficulty with the percolation
models of the structure formation is insufficient correlation on small scales since it does
not take into account of the inter-galaxy gravity.
Key Words: Large scale structure, Correlation Function, Self-organized Criticality, Percolation
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