[HN Gopher] Behavior of spin glasses ___________________________________________________________________ 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. ___________________________________________________________________ (page generated 2022-11-12 23:00 UTC)