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November 21

Griffiths in math and physics

There's something called the Griffiths phase. If you search for griffiths phase activity so, you'll find things with similar names. A Griffiths singularity, Griffiths effects, there's probably more than one thing people call Griffiths' formula since there's a physicist called Phillip and two named David J. Griffiths. How many things are we dealing with under this name? Is there a book where they're all listed right next to each other? Gongula Spring (talk) 19:37, 21 November 2024 (UTC)[reply]

The concept of a Griffiths phase is named after theoretical physicist Robert B. Griffiths, who was the first to describe the appearance of such phases in an Ising model of ferromagnetism.^[1] He is also the eponym of the Griffiths inequality. Most uses of Griffiths singularity and Griffiths effect appear to be related. "Griffiths' formula" is a very general name that may refer to various formulas found by mathematicians with the surname Griffiths, such as Griffiths' integral formula for the Milnor number of an isolated hypersurface singularity, found by pure mathematician Philip A. Griffiths, also the eponym of the Griffiths group. See also Griffiths' theorem, named after yet another Griffiths. --Lambiam 23:43, 21 November 2024 (UTC)[reply]

That formulation seems at least superficially be leading to references to Alan Arnold Griffith. Formulas like ohmic or non ohmic dissipation in metallic griffiths phases used at the National High Magnetic Field Laboratory then tend to appear ambiguous to that effect too. Most other examples are deeply plunging into statistical quanta states thus unambiguously associated with Robert B. Griffiths instead. --Askedonty (talk) 00:13, 22 November 2024 (UTC)[reply]

The bracketing is not as in ((Griffith phase) field theory) but like (Griffith ((phase field) theory)), a theory of fracture, based on a phase-field model, developed by Griffith. --Lambiam 08:47, 22 November 2024 (UTC)[reply]

The interesting thing is that those approaches are leading us very near of a (a least to me ) finally rather satisfying view of the problematics induced by the idea of Action at a distance. --Askedonty (talk) 10:51, 22 November 2024 (UTC)[reply]

So much that you only have to think about it and what do you get? Long distances in apparent contradiction to.. --Askedonty (talk) 11:00, 22 November 2024 (UTC)[reply]

I'm not sure if these long distances anticipate my next question, which is what does "long-range" mean in the search results above?

Gongula Spring (talk) 15:54, 22 November 2024 (UTC)[reply]

Perhaps, as in #16 from that request as I get it "Temporal disorder in discontinuous non-equilibrium phase transitions: general results". The "long distances" discussion above being from 2002 by contrast. --Askedonty (talk) 16:39, 22 November 2024 (UTC)[reply]

Number 16 uses "temporal" and "critical" terms, are we getting toward ideas about long-range temporal correlations in critical brain dynamics? Are they spooky?

Gongula Spring (talk) 17:05, 22 November 2024 (UTC)[reply]

I don't think so. Or not so directly anyway. Number 16 seem to be about logic and geometry: distance in that context is fact, and can also be manipulated. Relevant quote if there was one regarding our subject - but their process define a temporal Griffiths inactive phase some time - relevant would be (see their pdf):

Disorder due to spatial or temporal inhomogeneities is almost an unavoidable ingredient in many real systems, it is then desirable to understand their effects on these phase transitions. For continuous phase transitions, it was earlier recognized that spatial and temporal disorder changes the critical behavior whenever the generalized Harris criterion is violated [11, 12]: quenched spatial disorder is relevant whenever dν⊥ > 2 is violated while temporal disorder is relevant when νk = zν⊥ > 2 is violated; with ν⊥, νk and z being critical exponents of the clean phase transition and d being the number of spatial dimensions. Since the critical exponents of the directed percolation universality class violate the Harris criterion, it was then argued that this was the reason why it was never seen in experiments [13] (see however Ref. 14).

(They describe their purpose as: Non-equilibrium phase transitions have constituted a rich and lively topic of research for many years. They occur in a wide variety of models in ecology [1], epidemic spreading [2], sociophysics [3], catalytic reactions [4], depinning interface growth [5, 6], turbulent flow [7], among other fields [8–10].) [8–10] refer to Nonequilibrium Phase Transitions in Lattice Models. Sociophysics is a product of Positivism#Logical positivism ( perhaps note there a spooky "component not derived from observation" ) --Askedonty (talk) 21:03, 23 November 2024 (UTC)[reply]