Talk:Berezinskii–Kosterlitz–Thouless transition

message: Any chance to mention V.L. Berezinskii (who showed the existence of phase transition and demonstrated the role of vortices)?
I just did an ambiguation page for Thouless. How about something that tells us what field this is? maybe "...interacting spin systems in theoretical physics of the electron". (That's wrong no doubt, but you get my drift? Thanks --Singkong2005 03:08, 20 December 2005 (UTC)

message: I am experimentalist working in superconductivity, but for me it is hard to understand this explanation (language).
For example, "...This is because the expected ordered phase of the system is destroyed by transverse fluctuations".....what transverse fluctuations? 
Further "the Goldstone modes (see Goldstone boson) associated with this broken continuous symmetry". Which "this" symmetry?
In analysis, what is S^1? What is "universal cover R"?
Then, the positions of the vortices are denoted by x_i, then they become z_i??? Can it be explained how this transition is done? I assume that real and imaginary axes are just x and y axes in our 2D problem.
It is written "it is easy to see that the second term is positive infinite". For me it is not so easy to see, although I can guess that gradient is constant all over, so it integrates to infinity. But what about "branch cuts"? do we ignore them or what?
How the expression with logarithm was obtained?
The phrase "This is nothing other than a Coulomb gas". What this? The sum above? 
In the last paragraph I found a hint that vortices can actually move as a result of fluctuations or something? So, what are the assumptions? Can they be fully formulated?
In summery, the present version can be understood only by specialists and very mathematical. It does not look like a an enciclopedia article which can be read and understood by a student studying e.g. atomic physics.
Edward 21:45, 25 November 2006 (UTC)
replies: text: Goldstone bosons and symmetry breaking are cool, but I shouldn't have to look at the citations to make sure I'm not editing a math page. The justification for the KT transition using thermodynamics is a good start, but maybe we should include something in the intro that actually says plainly what it is and what systems we see it in.(Example: Josephson Junction arrays.)Duergan (talk) 06:19, 22 August 2011 (UTC)
thread_title:  hardly understandable 

message: It's odd to see an article on the KT transition that doesn't include vortex anti-vortex pairs, as most of the experimental papers I've seen are concerned with KT transition from lower energy bound pairs to higher energy dissociated pairs.  — Preceding unsigned comment added by Duergan (talk • contribs) 16:47, 22 August 2011 (UTC)
thread_title:  Vortex-Antivortex Pairs

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message: It's not clear what z_i (some complex value at the defect location)  z (value of some complex quantity ... everywhere else?) are.  Perhaps \phi is meant? A similar formulation is not used in any of the sources. CyreJ (talk) 06:54, 15 August 2020 (UTC)
thread_title:  variable z