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Categorizing condensed matter physics and statistical mechanics? How does one differentiate between these two? Can statistical mechanics be considered as a particular sub-field in condensed matter physics?

Why is it so rare to see a research group on statistical physics/mechanics? But there will always be a condensed matter physics research group?

How about complex and non-linear systems? Chaos theory? Are they considered a field in condensed matter physics as well?

I'm particularly interested in the studies of the interactions of many body/nodes/objects that would lead to a collective behaviour like phase transition level like the Ising models. I am also interested in systems that are very random/disordered like chaotic systems. I want to learn more about entropy during graduate studies but I am not really sure how to express my interest in terms of "field".

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  • $\begingroup$ Well, one can certainly make an argument that condensed matter physics is a subfield of statistical physics, but the reversed inclusion is obviously nonsensical. Similarly, neither complex and nonlinear systems, nor "chaos theory" can be considered as subfields of condensed matter physics. (Of course, ideas and methods from these various fields can be used in the latter.) $\endgroup$ – Yvan Velenik Dec 3 '17 at 14:54
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So physics is often all in one big dialogue with each other and these distinctions are much more nebulous than one would like, but there has been an informal classification where there are a bunch of subfields: condensed-matter physicists are very different from particle physicists, who are very different from biophysicists; one could easily add plasma physics, nuclear physics, fluid dynamics, and optics to these. But it's all really "airy-fairy", there are no firm boundaries.

Just to take as an example, particle vs condensed-matter physics, you might say "particle physics has to deal more with relativity, and a "zoo" of different particles with different statistics, and string theory; condensed matter physics has to deal more with statistical mechanics and all of the quasiparticles and such that you see in superconducting theory and beyond." This is independent of the different needs that both fields have in order to run experiments; you could expect to see a condensed-matter experimentalist in a cleanroom building an array of nanoscale devices; that's a world different from, say, a synchrotron where the whole building is the experiment.

But then if you poke at those criteria you would find that none of them were all that good. That superconducting theory was the inspiration for the electroweak unification and the Higgs mechanism; now you will find condensed-matter physicists importing the AdS/CFT correspondence from string theory and speaking of relativistic electrons in graphene and designing experiments to observe Majorana fermions: so much for all of these distinctions. They are subcultures which routinely talk to each other and you would not be able to come in like a biologist and clearly state "these are the lions, these are the leopards" with a clear separation between the two populations.

Statistical mechanics is one of the tools of physics-as-a-whole, it's got applications in plasmas and condensed matter and biophysics moreso than in optics and particle physics: but it has some applications there too (lasing and some of the Big Bang cosmology discussions come to mind).

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Complementing CR Drost's answer, with respect to the question:

How about complex and non-linear systems? Chaos theory? Are they considered a field in condensed matter physics as well?

No, certainly not.

Chaos Theory is part of Dynamical Systems theory, a branch of mathematics with applications in all sort of fields (see also this Math.SE question and this too). And it's a part of Physics too, at least in the senses that:

  1. Physicists like to apply the modus operandi of Physics to the field, as they do with so many others; and
  2. Dynamical Systems is obviously relevant to a science that occupies itself so much with finding equilibrium states and describing systems' evolution with time (or time-like variables).
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