Timeline for Non-renormalizable theory and mean field theory
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 14 at 1:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 12 at 15:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 12, 2023 at 2:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 24, 2021 at 9:00 | history | tweeted | twitter.com/StackPhysics/status/1396752858830213121 | ||
| Jun 26, 2020 at 21:37 | answer | added | vik | timeline score: 1 | |
| Jun 3, 2020 at 20:51 | comment | added | Abdelmalek Abdesselam | I didn't say the two problems are not related. What I wanted to make is the OP is aware there are two and not just one problem. Indeed, the relation is the direction of the RG flow going towards instead of away from the Gaussian fp. This direction explains both the mean field behavior in the IR problem and the triviality issues in the UV problem. | |
| Jun 3, 2020 at 20:49 | comment | added | Peter Kravchuk | @AbdelmalekAbdesselam There is still some indirect relation, no? Take the Ising lattice model. The IR fixed point of the phase transition in $d<4$ is described by a non-trivial Ising CFT. This Ising CFT fixed point can also be reached from the Gaussian fixed point by a relevant perturbation. Now, at $d=4$ these two points merge together, and this is related to the fact that the Gaussian fixed point looses one of the relevant operators ($\phi^4$). After the fps merge, the IR fp of the lattice becomes the gaussian fp. Still, I agree in that I can't see a direct relation between the two problems. | |
| Jun 3, 2020 at 20:42 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
edited title
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| Jun 3, 2020 at 20:39 | comment | added | Abdelmalek Abdesselam | There are two problems mixed up here: constructing field theories in the continuum (UV problem), and studying large scale properties of lattice spin systems (IR problem). In high dimension the IR problem simplifies and critical exponents are exactly equal to what one finds in mean field theory. However, the UV problem can't be solved, i.e., the only continuum limits one can hope to get are trivial. | |
| Jun 3, 2020 at 20:18 | history | asked | lol | CC BY-SA 4.0 |