[HN Gopher] Mathematicians Prove Symmetry of Phase Transitions
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Mathematicians Prove Symmetry of Phase Transitions
Author : pseudolus
Score : 77 points
Date : 2021-07-09 11:17 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| SilasX wrote:
| Anyone know if this has implications for P=NP, where they've
| found parallels between phase transitions and the "danger zone"
| of NP-complete problems?
|
| Background: for the NP-complete 3SAT (Boolean satisfiability
| where the clauses all have up to 3 terms OR'd together), there
| are ratios of clauses to variables that make instances trivially
| satisfiable or or trivially unsatisfiable. In between them are
| the hardest cases, where you run into exponential time blow-up.
| That transition is analogized to phase transitions in matter.
| Aardwolf wrote:
| Is this the kind of symmetry to which Noether's theorem applies?
| If so it should come with a conservation of something. Any idea
| of what?
| nautilius wrote:
| A rotational symmetry implies conservation of angular momentum.
| Aardwolf wrote:
| But we already know which symmetry is related to angular
| momentum, or do you mean a different kind of angular momentum
| related to phase transitions?
| ganzuul wrote:
| What would scale symmetry conserve? Entropy?
| scarmig wrote:
| A relevant discussion that I'm digesting:
|
| https://physics.stackexchange.com/questions/2670/what-is-
| the...
| codethief wrote:
| The link doesn't seem very relevant. A scale-invariant or
| even conformally invariant universe is something
| completely different from some substance exhibiting
| (approximate[0]) conformal invariance during a phase
| transition.
|
| [0]: The paper from the article explicitly refers to
| "rotational invariance at large scales".
| codethief wrote:
| I don't think it is. Physicists often summarize Noether's
| Theorem as "A symmetry implies the existence of a conserved
| quantity" but really what Noether's Theorem refers to are
| symmetries of a physical system's action[0]. I don't know a lot
| about phase transitions but judging from the article and the
| linked references, the symmetry we're talking about here
| doesn't seem to be a symmetry of any action.
|
| [0]: https://en.wikipedia.org/wiki/Action_(physics)
| TheRealPomax wrote:
| No, they don't.
|
| > in a proof posted in December, a team of five mathematicians
| has come closer than ever before to proving that conformal
| invariance is a necessary feature of these physical systems as
| they transition between phases. The work establishes that
| rotational invariance -- one of the three symmetries contained
| within conformal invariance -- is present at the boundary between
| states in a wide range of physical systems
| findalex wrote:
| Is it implied that the different phase transitions of - say water
| - are related to the various ways symmetry can break? This makes
| sense intuitively, I think: Ice -> liquid you are changing size a
| bit but liquid water still has some transient structure at the
| molecular level; liquid -> gas you are changing size a lot and
| gaining rotational + translational invariance? These symmetries I
| think make sense if you think about water the individual water
| molecules are doing during the various phases.
| nimish wrote:
| Not necessarily:
| https://physics.stackexchange.com/questions/105166/symmetry-...
| 52-6F-62 wrote:
| Formal maths is not my strong point these days, so I'm reading
| this from a more abstract position, but it sounds like yet more
| pointers to systems being more than a sum of their parts.
|
| Am I understanding it correctly?
|
| This might just be my ignorance of the domain talking, but why
| would there be invariance across the form?
|
| What's the proposed rule beneath the rule of conformal
| invariance?
|
| Am I just whimsy to be reminded of Armani-Hamed's theories about
| particle scattering?
| raziel2701 wrote:
| I'm with you not being an expert and being unable to understand
| most of the lingo and the article. The conformal invariance
| example in the pictures spoke to me about the fractal nature in
| the universe. Fractality just keeps popping up in my readings
| and that may have colored my read of the article.
| mathgenius wrote:
| Yes, these when these models become critical (eg. where the
| distinction between liquid & gas goes away [1]) they form
| clouds of condensation at all scale sizes, so it is like a
| fractal.
|
| [1] https://twitter.com/johncarlosbaez/status/127591543287712
| 563...
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