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I still remember my condensed matter professor saying "The Kosterlitz-Thouless transition is the most important discovery in physics in the second half of the 2
by oneloop 10y ago
I still remember my condensed matter professor saying "The Kosterlitz-Thouless transition is the most important discovery in physics in the second half of the 20th century". Surely partly motivated by professional bias, no doubt, but there's still merit to the claim. If you believe that "all physics is either harmonic oscillators or phase transitions", the Kosterlitz-Thouless is the first example (I believe) of a phase transition that does not contain a local order parameter. Because of that certain materials proved illusive to all mathematical models of the time.
Related: Onsager received the 2000 Nobel Prize in Physics, also for 2D phase transitions. Trivia: Onsager was a Chemist! :D
EDIT: I believe this is the original paper:
http://iopscience.iop.org/article/10.1088/0022-3719/6/7/010/pdf http://iopscience.iop.org/article/10.1088/0022-3719/6/7/010/...
- okket 10y agoFYI, Wikipedia page about the Kosterlitz–Thouless transition: https://en.wikipedia.org/wiki/Kosterlitz%E2%80%93Thouless_transition https://en.wikipedia.org/wiki/Kosterlitz%E2%80%93Thouless_tr...
- deleted 10y ago[deleted]
- oneloop 10y agoI expect that article will see lots of improvement in the coming weeks/months.
- flashman 10y agoGood. It's one of those bloody articles that requires a layman to read all of the attached articles, two or three links deep, to have any chance of understanding just the parts without mathematical formulae. And before anyone accuses me of wanting to dumb down Wikipedia: yes, that's exactly what I want. Wikipedia should be written to a generalist audience, not by specialists for specialists. edit: I can't say it any better than this article: https://scholarlykitchen.sspnet.org/2012/09/24/wikipedias-writing-tests-show-its-too-sophisticated-for-its-audience/ https://scholarlykitchen.sspnet.org/2012/09/24/wikipedias-wr...
- oneloop 10y agoPhysics is complex man, what did you expect. If you know nothing, you need to learn a lot in order to even understand their starting point. And regarding wikipedia articles, there's two big design alternatives: for each article you either write into it all the necessary background, or instead link to the necessary background in different articles. I suspect that the modus operandi that wikipedia has chosen is that you should do the former for mainstream topics and the latter for niche topics.
- flashman 10y agoHere's a complex biology article that contains a lot of technical terms and links, yet still manages to be readable to a general audience: https://en.wikipedia.org/wiki/Leaf https://en.wikipedia.org/wiki/Leaf I get the feeling that most math-involving Wikipedia pages are simply compound regurgitations of various textbooks. > you need to learn a lot in order to even understand their starting point This is kind of a cop-out. In the coming days there will be reams written on these laureates in the scientific press, much of which will be more enlightening, informative and contextually relevant than the dedicated encyclopaedia article.
- oneloop 10y ago> I get the feeling that most math-involving Wikipedia pages are simply compound regurgitations of various textbooks. You are absolutely right, because writing quality original work takes effort, and writing quality original maths work takes 100x more effort. > This is kind of a cop-out Call it whatever you want, but the fact remains that some subjects are more complex than others. Complex matters take more effort to write about, and there's fewer people qualified to write about them. When these two factors come together, you see regurgitated stuff. If you think that everything is equally simple if you explain it the right way, you're sorely mistaken about the nature of reality. All this reminds me that I shouldn't be spending my own effort on HN :D
- euyyn 10y ago
- brennebeck 10y agoI'm curious, who was your professor?
- oneloop 10y agoProfessor at a third-world country University, you wouldn't know him.
- carlob 10y agohttp://mecklenburg.bol.ucla.edu/kosterlitz%20and%20thouless%20transistion.pdf http://mecklenburg.bol.ucla.edu/kosterlitz%20and%20thouless%... full text
- selimthegrim 10y agoIt would be an exaggeration, but not by much, to say I was crying tears of joy at my desk this morning. Onsager wasn't alive in 2000. If you want to get a start on understanding this, try considering the problem of BEC in 2D. The same logarithmic (algebraic, that is to say not exponential) divergence in that integral is at the heart of the BKT transition.
- kkylin 10y agoNitpick: Onsager died in 1976 [1]. Also, his Nobel citation credits his work on reciprocity relations [2] and, I suppose, by extension regression hypothesis and what we would now call fluctuation-dissipation theorem. His solution of the 2d Ising model was not mentioned (though to be sure a tour de force). [1] https://en.wikipedia.org/wiki/Lars_Onsager https://en.wikipedia.org/wiki/Lars_Onsager [2] http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1968/ http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1...
- sytelus 10y agoI'm intrigued by your quote "all physics is either harmonic oscillators or phase transitions". Could you please elaborate on that? Just looked up online sources but can't seem to find this quote anywhere.
- Certhas 10y agoConsider a system that is slightly perturbed from its resting place. If it returns to its previous resting place it's a (damped) harmonic oscillator (or an infinite collection of them = a free field). If it doesn't, and it looks different than before, then it underwent a phase transition described by Landau-Ginzburg theory. Obviously this is not exhaustive. But it gets you further than you naively think it should. Let's look at the harmonic oscillator, why is the thing probably a harmonic oscillator? Well the potential is typically an analytic function, and we are near a resting point, so the linear order in the Taylor expansion vanishes and the potential is approximately V(x) ~ x^2. Harmonic oscillator. Say you want to look at a quantum field theory. Well actually defining one is hard. The only case where we know how to is for a free field theory. And a free field theory is actually a collection of harmonic oscillators. Now interacting QFT, which underlies all of observed matter, is built by gluing together harmonic oscillators in a clever way. You know Feynman diagrams? The lines in a Feynman diagram represent the particle behaving as if it was made up of independent harmonic oscillators (free field). At the vertices we just bump the harmonic oscillators around a bit. So standard QFT is a very clever shuffling around of harmonic oscillators (lots of group representation theory organises the shuffling, and several Nobel prizes worth of physics are contained in the details). Obviously there is plenty of physics that does not fit into either of these paradigms (GR, non-linear dynamical systems, atomic and molecular physics). But they both are utterly fundamental and enormously powerful tools in two very prominent branches in physics: High energy and condensed matter.
- oneloop 10y agoAnother way to put it would be that "all physics is either perturbative or non-perturbative", although this one doesn't sound as catchy since it is transparently a tautology ;-)