4 ms·

Here's the preprint of the article in Phys. Rev. Lett. that this is a press release for. Note that it's been on arXiv for almost a year now. Also note PRLs are

Here's the preprint of the article in Phys. Rev. Lett. that this is a press release for. Note that it's been on arXiv for almost a year now. Also note PRLs are brief and not very detailed, so it should be readable for physicists not working in this particular field. https://arxiv.org/abs/1607.04217 https://arxiv.org/abs/1607.04217 Edit, TL;DR: Yaida found that for mean-field models of spins with quenched impurities in an external magnetic field, in three dimensions, the renormalization group flow admits a fixed point at the two-loop level of calculation. It was long known that a fixed point exists in dimensions d > 6, but earlier one-loop calculations didn't find one for d=3, so it was thought that the nice results from these mean-field models had no physical relevance. This new result indicates that we can indeed use these models to understand physical disordered systems.

schoen 9y ago
Can you give a suggestion for understanding the connection between magnetic fields and glass? Do we need to understand quantum physics in order to properly appreciate this connection?
- semi-extrinsic 9y ago
  Physicists extend "glass" into "disordered systems". A system can be ordered or disordered in different way, e.g. order (crystal) or disorder (glass) in the positions of atoms, or the simpler case of ordered or disordered spins of atoms (either "up" or "down"). The same phenomena exist in both fields, e.g. glass transitions, so we prefer to study the simpler "implementation", namely spins in a magnetic field. Computer analogy: we're trying to reverse-engineer an alien ASIC, which can operate either on an array of tuples of three reals, or on an array of bools. It works approximately the same in both cases. The latter case is much easier to analyze, so we prefer to do that.
  - deepnet 9y ago
    Analogously Neural Network learning, i.e. learning modeled as a phase transition between disorder and order: “... studies the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model” from "The Loss Surfaces of Multilayer Networks" Choromanska, Henaff, Mathieu, Arous, & LeCun [1] [1] https://arxiv.org/abs/1412.0233 https://arxiv.org/abs/1412.0233 Also the physics of collapsing sand piles.
  - schoen 9y ago
    Thanks! The other comment also led me to https://en.wikipedia.org/wiki/Spin_glass https://en.wikipedia.org/wiki/Spin_glass, which I didn't know about at all (I'd heard the term once but had no context for it).

schoen 9y ago

Can you give a suggestion for understanding the connection between magnetic fields and glass? Do we need to understand quantum physics in order to properly appreciate this connection?

semi-extrinsic 9y ago
Physicists extend "glass" into "disordered systems". A system can be ordered or disordered in different way, e.g. order (crystal) or disorder (glass) in the positions of atoms, or the simpler case of ordered or disordered spins of atoms (either "up" or "down"). The same phenomena exist in both fields, e.g. glass transitions, so we prefer to study the simpler "implementation", namely spins in a magnetic field. Computer analogy: we're trying to reverse-engineer an alien ASIC, which can operate either on an array of tuples of three reals, or on an array of bools. It works approximately the same in both cases. The latter case is much easier to analyze, so we prefer to do that.
- deepnet 9y ago
  Analogously Neural Network learning, i.e. learning modeled as a phase transition between disorder and order: “... studies the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model” from "The Loss Surfaces of Multilayer Networks" Choromanska, Henaff, Mathieu, Arous, & LeCun [1] [1] https://arxiv.org/abs/1412.0233 https://arxiv.org/abs/1412.0233 Also the physics of collapsing sand piles.
- schoen 9y ago
  Thanks! The other comment also led me to https://en.wikipedia.org/wiki/Spin_glass https://en.wikipedia.org/wiki/Spin_glass, which I didn't know about at all (I'd heard the term once but had no context for it).