Universality and Scaling in Critical Systems

Abstract

In this talk, I first give a historical review of universality and scaling in critical many-body systems. I then review our works on universality, scaling, and superscaling in critical systems. The topics to be discussed include (1) universality and scaling in the percolation and the Ising models [1, 2, 3], (2) superscaling in the percolation model [4, 5], (3) universality and scaling in the self-organized critical systems, including earthquakes, sandpile model [6, 7], and literary works. Finally, I discuss the possibility to extend the ideas of universality and scaling to social systems. References [1] C.-K. Hu, C.-Y. Lin, and J.-A. Chen, Phys. Rev. Lett. 75, 193 (1995) and 75, 2786(E) (1995), Physica A 221, 80 (1995); C.-K. Hu and C.-Y. Lin, Phys. Rev. Lett. 77, 8 (1996); C.-K. Hu and F.-G. Wang, J. Korean Physical Soc. 31, S271 (1997); H. P. Hsu, S. C. Lin and C.-K. Hu, Phys. Rev. E 64, 016127 (2001); H. Watanabe, et al., J. Phys. Soc. Japan. 70, 1537 (2001). [2] Y. Okabe, et al. Phys. Rev. E 59, 1585 (1999); Y. Tomita, Y. Okabe, and C.- K. Hu, Phys. Rev. E. 60, 2716 (1999); C.-K. Hu, J.-A. Chen, and C.-Y. Lin, Physica A 266, 27 (1999); M.-C. Wu, C.-K. Hu, and N.S. Izmailian, Phys. Rev. E 67, 065103(R) (2003); N.S. Izmailian and C.-K. Hu, Phys. Rev. Lett. 86, 5160 (2001). [3] F.-G. Wang and C.-K. Hu, Phys. Rev. E 56, 2310-2313 (1997). [4] H. Watanabe, S. Yukawa, N. Ito, and C.-K. Hu, Phys. Rev. Lett 93, 190601 (2004). [5] H. Watanabe and C.-K. Hu, Phys. Rev. Lett, in press (2005). [6] C.-K. Hu, E. V. Ivashkevich, C.-Y. Lin, and V.B. Priezzhev, Phys. Rev. Lett. 85, 4048-4051 (2000). [7] C.-K. Hu and C.-Y. Lin, Physica A 318, 92-100 (2003).