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The phenomenon of spontaneous symmetry breaking is behind the standard model of particle physics... it turns out it is also behind the generative powers of diff

The phenomenon of spontaneous symmetry breaking is behind the standard model of particle physics... it turns out it is also behind the generative powers of diffusion models! Check out our latest blog post! https://gabrielraya.com/blog/2023/symmetry-breaking-diffusion-models/ https://gabrielraya.com/blog/2023/symmetry-breaking-diffusio...

evanb 3y ago
Is this more like a thermodynamic transition, or a zero-temperature quantum phase transition? Do you know anything about the thermodynamic limit? From your figures it seems that the phase transition second (or higher) order. If it's second+ order, have you measured any of the critical exponents? Any idea as to the universality class?
- tnecniv 3y ago
  Not the author but it seems like a thermal transition, given that they’re analyzing how the potential well evolves over time. Another interesting thought your second paragraph gave me is if you could do any RG stuff, which has had a lot of success in physics analyzing phase transitions and critical phenomena
  - evanb 3y ago
    A quantum phase transition is also like a change in a potential well; it's just that the control parameter is not temperature but some other parameter of the Hamiltonian. There is a lot known about universal critical phenomena, hence my question about the critical exponents. If they could show "oh yes this is in the such-and-such universality class" then suddenly I have a much greater understanding of what's up.
    - tnecniv 3y ago
      Do you have any recommended reading on critical phenomena? I’ve become quite interested in statistical mechanics lately, but my background is engineering / applied math. Thus, I learned information theory first and am interested in how physicists analyze statistical mechanics because it’s quite different from the rate-distortion theory I learned originally.
      - evanb 3y ago
        I don't have a good introductory reference, to be honest. I was first exposed to it (and RG) in my 2nd year in physics grad school, and to be frank did not understand it at all then (partly due to crap teaching).
- lucaambrogioni 3y ago
  Hi Evanb, I am an author of the paper. Formally speaking, the phenomenon we studied resembles a second l-order phase transition similar to those in ferromagnetic materials. Keep in mind though that there are differences white conventional thermodynamics. The most obvious one is that stricktly speaking, Theta cannot be interpreted as a temperature. Si said, the transition in the 1d example is almost identical to the mean field transition of the ising model (not surprising, it breaks the same symmetry group) No we didn't derive the critical exponents jet but we plan to do this kind of research in the future.
  - evanb 3y ago
    Do you really know it breaks Z2 rather than something else? There are plenty of symmetry breaking patterns that correspond to observables which go from <x^2> = 0 to (<x^2> ≠ 0 and <x> = ±some mean if you don't tunnel enough). If it really breaks Z2 and falls into the Ising universality class then you should be able to predict [read: look up] some of the critical exponents before measuring them.
    - lucaambrogioni 3y ago
      The 1d example certainly breaks Z2, but since the thermodynamics is slightly different, you need to careful. For example, several exponents regulate the scaling with respect to the temperature, but theta is not, strictly speaking, a temperature parameter. We need to do the calculations see.

evanb 3y ago

Is this more like a thermodynamic transition, or a zero-temperature quantum phase transition? Do you know anything about the thermodynamic limit? From your figures it seems that the phase transition second (or higher) order. If it's second+ order, have you measured any of the critical exponents? Any idea as to the universality class?

tnecniv 3y ago
Not the author but it seems like a thermal transition, given that they’re analyzing how the potential well evolves over time. Another interesting thought your second paragraph gave me is if you could do any RG stuff, which has had a lot of success in physics analyzing phase transitions and critical phenomena
- evanb 3y ago
  A quantum phase transition is also like a change in a potential well; it's just that the control parameter is not temperature but some other parameter of the Hamiltonian. There is a lot known about universal critical phenomena, hence my question about the critical exponents. If they could show "oh yes this is in the such-and-such universality class" then suddenly I have a much greater understanding of what's up.
  - tnecniv 3y ago
    Do you have any recommended reading on critical phenomena? I’ve become quite interested in statistical mechanics lately, but my background is engineering / applied math. Thus, I learned information theory first and am interested in how physicists analyze statistical mechanics because it’s quite different from the rate-distortion theory I learned originally.
    - evanb 3y ago
      I don't have a good introductory reference, to be honest. I was first exposed to it (and RG) in my 2nd year in physics grad school, and to be frank did not understand it at all then (partly due to crap teaching).
lucaambrogioni 3y ago
Hi Evanb, I am an author of the paper. Formally speaking, the phenomenon we studied resembles a second l-order phase transition similar to those in ferromagnetic materials. Keep in mind though that there are differences white conventional thermodynamics. The most obvious one is that stricktly speaking, Theta cannot be interpreted as a temperature. Si said, the transition in the 1d example is almost identical to the mean field transition of the ising model (not surprising, it breaks the same symmetry group) No we didn't derive the critical exponents jet but we plan to do this kind of research in the future.
- evanb 3y ago
  Do you really know it breaks Z2 rather than something else? There are plenty of symmetry breaking patterns that correspond to observables which go from <x^2> = 0 to (<x^2> ≠ 0 and <x> = ±some mean if you don't tunnel enough). If it really breaks Z2 and falls into the Ising universality class then you should be able to predict [read: look up] some of the critical exponents before measuring them.
  - lucaambrogioni 3y ago
    The 1d example certainly breaks Z2, but since the thermodynamics is slightly different, you need to careful. For example, several exponents regulate the scaling with respect to the temperature, but theta is not, strictly speaking, a temperature parameter. We need to do the calculations see.