Universality and scaling in physical, biological, and social systems

Abstract

The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors appear. In this talk, I first introduce the concepts of universality and scaling in critical physical systems, including ordinary critical systems [1] and self-organized critical systems [2]. I then briefly review some examples of universal and scaling behaviors in physical, biological, and social systems including universal mechanism for critical behavior of lattice systems [3,4], universal finite-size scaling functions of percolation [5] and Ising model [6], universal critical exponents and amplitude ratios [7,8], universal ratio of volume to surface area of proteins [9], universal mechanism for protein aggregation [10], glassy behavior of polymers and proteins [10,11], universal crossover behavior of stock returns [12], etc. Finally, I mention some interesting problems for further studies. [1] H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, New York, 1971); ?? C.-K. Hu, Chinese J. Phys. 52, 1-76 (2014). [2] P. Bak, How Nature Works? (Springer-Verlag, Berlin, 1996); C.-K. Hu, Chinese J. Phys. 52, 1-76 (2014). [3] C.-K. Hu, Physica A 119, 609 (1983); J. Phys. A: Math. Gen. 16, L321 (1983); Phys. Rev. B 29, 5103 and 5109 (1984). [4] C.-K. Hu and K.-S. Mak, Phys. Rev. B 39, 2948 (1989); Phys. Rev. B 42, 965 (1990). [5] C.-K. Hu, C.-Y. Lin, and J. A. Chen, Phys. Rev. Lett. 75, 193 (1995); C.-K. Hu and C.-Y. Lin, Phys. Rev. Lett. 77, 8 (1996); C.-Y. Lin and C.-K. Hu, Phys. Rev. E 58, 1521 (1998). ?[6] F. G. Wang and C.-K. Hu, Phys. Rev. E 56, 2310 (1997); Y. Okabe, K. Kaneda, M. Kikuchi, and C.-K. Hu, Phys. Rev. E 59, 1585 (1999); Y. Okabe, K. Kaneda, M. Kikuchi, and C.-K. Hu, Phys. Rev. E 60, 2716 (1999). [7] H. Watanabe, N. Ito, and C.-K. Hu, J. Chem. Phys. 136, 204102 (2012). [8] N.Sh. Izmailian and C.-K. Hu, Phys. Rev. Lett. 87, 084301 (2001). [9] M.-C. Wu, M. S. Li, W.-J. Ma, M. Kouza, and C.-K. Hu, EPL 96, 68005 (2011). [10] W.-J. Ma and C.-K. Hu, J. Phys. Soc. Jpn 79, 024005, 024006, 054001, 104002 (2010); C.-K. Hu and W.-J. Ma, Prog. Theor. Phys. Supp. 184, 369 (2010). [11] S. G. Gevorkian, A. E. Allahverdyan, D. S. Gevorgyan and C.-K. Hu, EPL 95, 23001 (2011); Sci. Rep. 5,13064? (2015). [12] W.-J. Ma, S.-C. Wang, C.-N. Chen, and C.-K. Hu, EPL 102,66003 (2013).