缪海兴， 张杨^*， 侯永辉

（  中国科技大学；  ）

Miao Haixing， Zhang Yang ^*， Hou Yonghui

（  University of Science and Technology of China；  ）

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 $P=P_c$, 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 $\xi(r)$, 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 $\sim k^{-2.1}$ on large scale, and $\sim k^{-2.6}$ 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 $\xi(r)$ 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.
Keywords： Large scale structure, Correlation Function, 

 

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