Talk:Phase transition

From the article:

The ferromagnetic transition is another example of a symmetry-breaking transition, in this case time-reversal symmetry. The magnetization of a system switches sign under time-reversal (one may think of magnetization as produced by tiny loops of electrical current, which reverse direction when time is reversed.) In the absence of an applied magnetic field, the paramagnetic phase contains no net magnetization, and is symmetrical under time-reversal; whereas the ferromagnetic phase has a net magnetization and is not symmetrical under time-reversal.

This isn't my area of expertise, but I'm pretty sure this is wrong. The direction of the magnetic field always reverses under time reversal, but that's because of the way the field is represented mathematically; it isn't a T violation. -- BenRG 05:51, 24 Sep 2003 (UTC)

I'm note sure what you mean by "that's because of the way the field is represented mathematically". Note that "symmetry breaking" has a narrow meaning in the context of the article. It refers to a symmetry that is unbroken by the underlying physical laws, being broken by a particular configuration of the system. In this case, the laws of electromagnetism are T-invariant, but magnetic systems break T invariance. To give another example, crystals break continuous translational symmetry, even though the physics of spacetime are symmetric under arbitrary spatial translations.

Is this what you're worried about? -- CYD

What I meant is just that the magnetic field is an axial vector field. I agree that symmetry breaking takes place in the ferromagnetic transition, but it's not time reversal symmetry that's broken. Time reversal symmetry is only broken by the second law of thermodynamics and (in a different sense) by weak interactions. The formation of ferromagnetic domains resembles crystallization and has the same symmetry-breaking properties (i.e. it breaks isotropy).

I've never heard time-reversal symmetry mentioned in the context of thermodynamic phase transitions, but if you can find a textbook that disagrees with me I'll reconsider my position. -- BenRG 08:48, 25 Sep 2003 (UTC)

It is fairly uncontroversial, at least in condensed matter physics, to say that magnetic systems break T. See, for example, p.18 of Basic Notions of Condensed Matter Physics by P.W. Anderson, and p.40-54 of Lectures on Phase Transitions and the Renormalization Group by N. Goldenfeld. (Both books have many profound things to say about the subject of phase transitions, by the way.)

Anyhow, your argument does not compute. You claim that magnetic systems cannot break T because T is only broken by the second law of thermodynamics and weak interactions. By the same token, no systems can break continuous translational symmetry, because that symmetry is unbroken by all known laws of physics; but this assertion is false, as demonstrated by the existence of crystalline solids (or, for that matter, by the inhomogenous distribution of matter in the universe.) -- CYD

Goldenfeld answered my objection in his very first sentence when he wrote: "The first symmetry which we discuss is up-down symmetry, sometimes called time-reversal symmetry or Z₂ symmetry." In other words, it's really about reversing the magnetic field, and time reversal is just one (theoretical) way to describe that. I interpreted "time reversal" to mean reversing the evolution of a dynamic system, and in that sense it's a little weird to say that any static system (like a ferromagnet in thermal equilibrium) violates time reversal symmetry.

I propose that the paragraph be changed to something like this:

Another symmetry which can be broken by a phase transition is "up-down symmetry" or "time-reversal symmetry", which is symmetry under the reversal of the direction of electric currents and magnetic field lines. This symmetry is broken by the appearance of magnetized domains in the ferromagnetic transition. The name "time-reversal symmetry" derives from the fact that electric currents reverse direction under negation of the time coordinate.

I'm not sure that I phrased it too well, but the three main changes are: 1. Makes the symmetry, rather than the phase transition, the topic of the paragraph (otherwise it's unclear why the paragraph doesn't mention that the ferromagnetic transition also breaks isotropy); 2. Removes the link to the T-symmetry article, which is about a different symmetry entirely; 3. Clarifies that time reversal is just one way of looking at the symmetry in question. Is this acceptable?

By the way, I agree that what I wrote above beginning "Time reversal symmetry is only broken by..." is nonsense. What I was trying to articulate is that physicists don't normally talk about time-asymmetry in actual physical systems because it's ubiquitous. To say that a physical law violates time-reversal symmetry is to say something interesting and meaningful because there are so few that do; but to say that a particular system violates it is to say very little. I agree, though, that it does make sense to talk about it in this context. Sorry. -- BenRG

Your paragraph looks okay. I'd make a few modifications, like this:

Another example of a symmetry that can be broken by a phase transition is "up-down symmetry", also called "time-reversal symmetry", meaning symmetry under the reversal of the direction of electric currents and magnetic field lines. This symmetry is broken during the transition to a ferromagnetic phase, due to the formation of magnetic domains in which individual magnetic moments are aligned with one another. Within each domain, the magnetic field points in a fixed direction chosen during the phase transition. The name "time-reversal symmetry" comes from the fact that electric currents reverse direction when the time coordinate is reversed.

I seem to be having some sort of technical problem with editing the article, so why don't you go ahead and make whatever change you like. -- CYD

--- Shouldn't the various terms for the various phase transitions be noted and defined or at least linked-to in this article? ie. condensation, melting, boiling, sublimation etc?? I was trying to find the term for solid -> gas transition (sublimation) and had to resort to google because the obvious place for it to me (this article) had no mention of the term...

--- The wikipedia term order parameter gets redirected to this page. Perhaps another page should be created for it? The order parameter is a relatively new concept that can be a rich source of future work. For instance, in systems with quenched disorder, such as a glass, below T_c, the system is split into multiple ergodically-separated phase regions. A single-valued order parameter would be meaningless in this case. In replica techniques, the order parameter of this glass would be described by an N x N matrix where N is the number of replicas. (Also, <math> N \rightarrow 0 <math>, but that's another story.) Wilgamesh 22:51, 18 Sep 2004 (UTC)

That would be great. Would you like to do it? Btw, it is not a true statement that the order parameter is a new concept. Landau introduced it way back in 1936. -- CYD

Right, I only mean that it's a relatively new term, and that it's by no means something that's fixed in stone. cf partition function. I guess I'm stuck in Landau's age. Oh, I thought of another thing, like in liquid crystals, there's a nematic phase: picture rods aligned, but not all in plane. Since rods are the same under inversion, a vector is inappropriate as an order parameter. Instead we must use a matrix. Wilgamesh 19:22, 21 Sep 2004 (UTC)

Depends on what you mean by "relatively new", I suppose. The venerable statistical mechanics text of Landau and Lifshitz talks about the "order parameter". Even the idea that the order parameter can be something other than a simple real number is not that new: AFAIK the first non-trivial order parameter was the superconducting order parameter, a complex scalar. That was introduced in 1950 by the Ginzburg-Landau theory, though it was only explicitly identified as an order parameter by Gor'kov around 1955, I think. By the way, I believe the order parameter for nematics is more succinctly described as a line element (a vector without an arrow.) -- CYD

Contents

1 Diagrams 2 Higher-order phase transitions 3 liquid/gas possible confusion 4 Ehrenfest classification

Diagrams

It would be nice to include sample (possibly schematic) phase diagrams for a few typical systems, e.g. water (P vs. T), a ferromagnet (H vs. T), and superconductivity (H vs. T). The same diagrams should be included on the respective pages, and perhaps discussed in more detail there. Steven G. Johnson 21:28, 24 Mar 2004 (UTC)

Higher-order phase transitions

The article represents third and higher order phase transitions as a theoretical possibility. Have they actually been observed in practice? --137.111.13.34 22:47, 14 Oct 2004 (UTC)

It may have been. It seems that the signature of a higher order phase transition is sometimes easy to overlook. There is some indication (Physical Review Letters, 1999) that the appearance of superconductivity in BaKBiO3 is a fourth order phase transition.

liquid/gas possible confusion

Most people probably think of the liquid/gas system as having a first order phase transition. I think a couple of extra sentences could help explain what is continuous in this system. Ie the change in density across the phase coexistance line as a function of (T-Tc). Although I'm not confident enough that I won't make it worse to clarify this myself.

Er, it is a first-order transition (except at the critical point). -- CYD

Ehrenfest classification

Ehrenfest's classification of Phase Transitions does not have anything to do with mean field theory (or any other approximation method), contrary to what the author says. It's based on analytic properties of the EXACT free energy.