Tue, 10 Oct 2023
16:00 - 17:00
Nicola Kistler
Goethe University Frankfurt
The replica method, together with Parisi symmetry breaking mechanism, is a powerful tool which allows to compute the limiting free energy of any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the procedure, and which allows to represent the free energy of virtually any model from statistical mechanics as a Gaussian mixture model. I will then conclude with some remarks on the ensuing “Babylonian formulas” in relation with : 
1) work by Dellacherie-Martinez-San Martin on M-matrices, potential theory and ultrametricity, the latter being the key yet unjustified assumption of the whole Parisi theory; 
2) work of Mezard-Virasoro suggesting that the onset of scales and the universal hierarchical self-organisation of random systems is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.
Please contact us with feedback and comments about this page. Last updated on 26 Sep 2023 11:15.