Leo Kadanoff passed away on October 26, 2015.

Leo Kadanoff is an American physicist in University of Chicago. His most prominent work is the idea of block spin and coarse-graining in statistical physics. [Kadanoff 1966] His work has an enormous impact on second-order phase transition and critical phenomena, based on the knowledge of scale and universality. His idea was further developed into renormalization group (RG), [Wilson 1983] which leads to Ken Wilson awarded with Nobel Prize in Physics in 1982.

The concept of RG has also been used to explain how deep learning works, [Mehta, Schwab 2014] which you can read more about from my previous blog entry and their paper. While only the equivalence between RG and Restricted Boltzmann Machine was rigorously proved, it sheds a lot of insights about how it works, in a way that I believe it is roughly what happens. Without the concept that Kadanoff developed, it is impossible for Mehta and Schwab to make such a connection between critical phenomena and neural network.

He has other contributions such as computational physics, urban planning, computer science, hydrodynamics, biology, applied mathematics and geophysics. He has been awarded with the Wolf Prize in Physics (1980), Elliott Cresson Medal(1986), Lars Onsager Prize (1998), Lorentz Medal (2006), and Isaac Newton Medal (2011).

His work has a significant impact on statistical physics, including problems of second-order phase transition, percolation, various condensed matter systems (such as conventional superconductors, superfluids, low-dimensional systems, helimagnets), quantum phase transition, self-organized criticality etc. To learn more about it, I highly recommend Shang-keng Ma’s *Modern Theory of Critical Phenomena* [Ma 1976] and Mehran Karder’s *Statistical Physics of Fields*. [Karder 2007]

Rest In Peace!

- L. Kadanoff, “Scaling laws for Ising models near T
_{c}“,*Physics***2**, 263 (1966). [See: http://jfi.uchicago.edu/~leop/SciencePapers/Old%20Science%20Papers/Scaling%20Laws%20for%20Ising%20Models%20Near%20Tc.pdf] - K. G. Wilson, “The renormalization group and critical phenomena”,
*Rev. Mod. Phys.***55**, 583 (1983). - Nobel Prize in Physics 1982.
- P. Mehta, D. J. Schwab, “An exact mapping between the Variational Renormalization Group and Deep Learning”, arXiv:1410.3831 (2014).
- K.-Y. Ho, “MathAnalytics (2) – Learning by Zooming Out“, WordPress (2015).
- S.-K. Ma, “Modern Theory of Critical Phenomena”, Advanced Book Program (1976).
- M. Karder, “Statistical Physics of Fields”, Cambridge (2007).
- Wikipedia: Leo Kadanoff – https://en.wikipedia.org/wiki/Leo_Kadanoff
- Leo Kadanoff’s Homepage in University of Chicago: http://jfi.uchicago.edu/~leop/

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