Talk:Mermin–Wagner theorem

Untitled

In the Heisenberg model example, the infinite magnetization is only an artifact of using the linear approximation. Maliz 21:12, 12 November 2006 (UTC)

The section on the Heisenberg model needs rewriting, but I am not an expert on the Heisenberg model. Maliz 21:23, 12 November 2006 (UTC)

For an expert on the Mermin-Wagner theorem please ask ...

... one of the authors (Herbert Wagner) himself; he is in Munich at the LMU university. You can also ask Patrick Bruno at the Max-Planck Institute at Halle, Germany. The present article seems rather good. -- 132.199.38.104 12:01, 12 October 2007 (UTC)

Consider changing the title

The reference by Halperin gives a history of the Mermin-Wagner theorem and points out that Hohenberg in fact submitted his paper first, and further that Mermin and Wagner not only were aware of the work, but said they were inspired by his work. Unfortunately, due to the slow referee process the Mermin-Wagner paper was published first. However, the community should probably agree that calling it "Mermin-Wagner" is not appropriate and it shoudl be called "Hohenberg-Mermin-Wagner" theorem. I think we should change the title of this page correspondingly. — Preceding unsigned comment added by 163.1.246.246 (talk) 19:27, 30 April 2021 (UTC)

Kosterlitz-Thouless transition

I don't understand the statement in the "Kosterlitz-Thouless transition" section that there can be an ordered phase without spontaneous symmetry breaking. Does this refer to a trivial (e.g. s = 0) ordered phase (which is not admissible for any systems where the spin has fixed magnitude)? How can there be an ordered phase which isn't killed by fluctuations? Woodford 07:04, 3 December 2007 (UTC)

That was at best a poor wording of the situation. The XY model at low (nozero) temperature has quasi-long-range order (rational decay of correlations, so infinite range correlations in a certain sense) but this isn't an ordered phase as would generally be understood, trivial or otherwise. Rafaelgr (talk) 22:49, 8 February 2008 (UTC)

I tried to reformulate and extend this section. Hope that illuminates the nature of the transition. — Preceding unsigned comment added by Cm.albrecht (talk • contribs) 12:39, 5 February 2013 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Mermin–Wagner theorem/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

The section about the Heisenberg model is as detailed as needed. The treatment is correct and follows the standard literature. I think the part in the introduction after the proof of the IR divergence is inappropriate for a discussion of the MW theorem. In addition, language needs to be added that the theorem pertains to continuous, global bosonic symmetries; supersymmetry can be broken in low dimensions, as can gauge symmetries (these latter being somewhat different, since gauge symmetries are never actually symmetries of the S-matrix).

Last edited at 01:39, 1 January 2012 (UTC). Substituted at 23:43, 29 April 2016 (UTC)

Title

This has been said before, Hohenberg came up with the theorem. Mermin and Wagner have often said this even in their paper. Sadly, Hohenberg got it published a year later. In Mermin's works he has always insisted that this should be called Hohenberg–Mermin–Wagner theorem, and maybe this article should be changed to reflect that. ReyHahn (talk) 11:28, 11 January 2024 (UTC)