[HN Gopher] Behavior of spin glasses
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       Behavior of spin glasses
        
       Author : Brajeshwar
       Score  : 36 points
       Date   : 2022-11-12 14:48 UTC (8 hours ago)
        
 (HTM) web link (phys.org)
 (TXT) w3m dump (phys.org)
        
       | WJW wrote:
       | I absolutely adore that we can predict these systems very well in
       | infinite dimensions and some cutting-edge theories can perform
       | well down to only 8 dimensions, but theories describing the
       | behavior of 3-dimensional systems are apparently still some way
       | off and may be impossible.
       | 
       | This reminds me of one of my favorite mathematician jokes: A
       | doctor is invited to a maths conference by their mathematician
       | friend. After they come out of one particularly difficult talk
       | about 12-dimensional string theory they ask their friend: "It was
       | very interesting but how can you possibly visualize a
       | 12-dimensional system???!?". The friend replies: "Oh it's quite
       | simple really: you just visualize an N-dimensional systems and
       | then set N=12!".
        
         | zitterbewegung wrote:
         | Honestly it's best to visualize a n dimensional system by a
         | bunch of sliders that can have various values. Like in 4d to
         | visualize that system you have a rotation slider similar to a
         | movie but the axis isn't time.
        
           | hobs wrote:
           | Why not just a spreadsheet? I guess that might not be
           | visualization...
        
           | PaulHoule wrote:
           | Why visualize it when you can just compute an integral?
           | 
           | https://phys.libretexts.org/Bookshelves/Thermodynamics_and_S.
           | ..
        
         | modeless wrote:
         | Geoff Hinton gave this wisdom in one of the lectures of his
         | legendary Coursera deep learning course: "To deal with hyper-
         | planes in a 14-dimensional space, visualize a 3D space and say
         | 'fourteen' to yourself very loudly. Everyone does it."
        
         | PaulHoule wrote:
         | Generically in the theory of phase transitions and critical
         | phenomena the infinite dimensional case is easy because mean
         | field theory works, but there is some dimension at which that
         | breaks, frequently N=6, and you can write an asymptotic
         | expansion in N-e for the critical exponents which converges
         | enough for most things that you can get the right answers in 3
         | dimensions.
         | 
         | We worked through this book when I was in grad school...
         | 
         | https://www.amazon.com/Theory-Critical-Phenomena-Introductio...
        
         | onos wrote:
         | Problem with these systems is that you can't study their
         | equilibrium with simulations. That's cause their equilibrium
         | time scale gets longer and longer as you lower temp and it
         | becomes too expensive to simulate long enough to get there. So
         | it's all theory and there are no models yet that can be fully
         | characterized analytically.
        
         | carlob wrote:
         | To be fair the mean field, or infinite dimensional version of a
         | lattice system is fairly easy to visualize, because it's just
         | the complete graph.
        
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