Why are critical phenomena important in physics?

[petergreat]

As someone who has studied little about this subject, I'm posting a naive question. Given that most natural phenomena occurs far away from phase transition, why are people so interested in the tiny region around phase transition? Why are critical phenomena considered so important and interesting? For example, do critical exponents have any real-world application?

 

[Dr Transport]

Because that is where the most interesting physics lies

 

[petergreat]

Because that is where the most interesting physics lies

Interesting but how? My rudimentary contact with the subject includes some basic Landau theory and Ising model scaling behavior, which seem innocent enough, but I just don't see the big picture - Why on Earth is this such a hot field of research? Can you explain to an outsider what's charming about this subject? What are the surprises, excitements and mysteries in this subject? Unlike subjects such as cosmology, there are few popular science articles aimed towards non-experts. That's why I'm asking here.

 

[Dr Lots-o'watts]

Are you asking why understanding phase transitions are important?

Like if we were to design an airplane to reach the south pole, what kind of fuel, coolant, lubrication, brake fluid, and battery acid would we use? And could we design a wing surface that resists ice formation from supercooled water droplets?

Knowing the phase change temperatures of certain products is important, and by understanding how phase transformation happens, maybe the property can be tuned for specific applications.

 

[cgk]

Another matter is that there are beautiful theories for phase transitions; and these theories often do not require much hardcore quantitative analysis, because the exact numbers here are not that important. That is interesting to many physicists: Some study phase transitions "because they can".

So estimating some critical exponents is still possible, while in truth the exact microscopic mechanisms underlaying, say, crystal nucleation in NaCl solution, or the boiling of water, are still far from being understood.

 

[Dr Lots-o'watts]

And whether or not to salt cooking water before boiling is an issue that affects everyone.

 

[Catalyst3146]

The point seems to missed here (cgk is close). The reason why people study phase transitions (here I talk of continuous transitions) is twofold. First there is universality, essentially that some of the physical properties of the transition (such as the critical exponents, but not the transition temperature itself) depend very few details of the underlying, microscopics. The fact that almost none of the information in an actual system matters, save a few details, is an incredible fact, making a huge number of phase transitions understandable by a handful of minimal models. Now secondly, by studying the phase transitions (which is more tractable due to universality) one can hope to try and then gain some knowledge of the nearby phases themselves, by folding in some of the details.

 

[maverick_starstrider]

Yes Catalyst is very correct. When studying phase transitions one is not just concerned with where they occur and of what type they are but also between what phases there is a transitions between. By knowing what type of transition occurs one can make concrete statements about the symmetries and ordering/non-ordering of the two (or more) phases on either sides of the transition. This is very important since it can often be extremely difficult to determine, a priori from just a Hamiltonian or free energy, what phase a system will be in for various values of its parameters. For example, if you expect something is in a spin liquid phase for some values of its system parameters then you can check the transition around that phase, their order, and whether symmetries are suppressed/broken to deduce the correctness of your assumption.

 

[robert80]

As someone who has studied little about this subject, I'm posting a naive question. Given that most natural phenomena occurs far away from phase transition, why are people so interested in the tiny region around phase transition? Why are critical phenomena considered so important and interesting? For example, do critical exponents have any real-world application?

I believe for understanding of such a big change of the system is good to know all the factors that are yealding to it. Its the same as some reactions in Macroreactors do not occur, because of the diffusion limitation, if we put the microtubes and carry the reactions there, we are 1. in non linear invironment and 2.
some reactions occur in microtubes that are not occurring at all at macrostate. Diffusion process is not any more limiting factor. What I wanted to state is: That on smaller dimensions (space variable) a lot could change and there is simply a limit you have to cross.. Its the same as with minorly changing the parameters of the transition states...

 

[maverick_starstrider]

Adding to me previous post, critical exponent very much have applications. The critical exponents across a transition (and usually taken on either side of the transition) tell you the nature or divergences (or non-divergences) of parameters across a transition. This tells you information about the universality class and more important tells you about the symmetries (or symmetry breaking) occurring on across the transition (which gives you information about the phases on either side of the transition.