Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Physics
Atomic and Condensed Matter
Order parameter, symmetry breaking Landau style
Reply to thread
Message
[QUOTE="paralleltransport, post: 6564847, member: 589748"] [B]TL;DR Summary:[/B] I'd like to understand what people mean by an order parameter Hi all, I am somewhat familiar the Landau Ginzburg paradigm for phase transition. My understanding is that it is a phenomological model of 2nd order phase transitions by "guessing" that the free energy can be expanded a configuration integral (path integral) of a functional of a local order parameter. In math the guess would look like this: [FONT=STIXGeneral-Regular]exp([/FONT][FONT=STIXGeneral-Italic]F[/FONT][FONT=STIXGeneral-Regular])∝∫[/FONT][FONT=STIXGeneral-Italic]Dϕ[/FONT][FONT=STIXGeneral-Regular]exp(∫[/FONT][FONT=STIXGeneral-Italic]ddxL[/FONT][FONT=STIXGeneral-Regular]([/FONT][FONT=STIXGeneral-Italic]ϕ[/FONT][FONT=STIXGeneral-Regular]))[/FONT]exp(F)∝∫Dϕexp(∫ddxL(ϕ)) for some order scalar order parameter [FONT=STIXGeneral-Italic]ϕ[/FONT]ϕ. Once that is done, one can apply all the field theory technologies that studies such (path) integral (RG flow, fixed point etc...). However when I read papers, I notice there is no clear definition of what an order parameter [B]must satisfy [/B]beyond pheonomological consideration. I'd like to ask if the following must be true: 1) it must be 0 in some phase and non-zero in the phase that breaks the symmetry. Therefore defining an order parameter must be [I]with respect to some broken symmetry.[/I] 2) it can be local or non-local although landau symmetry breaking theory is concerned with local order parameter ([I]for example, Wilson loop expectation value and Chern Numbers [/I]are non-local order parameters). 3) it must be a physical quantity (for gauge theories, one cannot use charged operators as order parameter since they transform non-trivially under the gauge group)... this seems a bit like a tautology but people often cite elitzur's theorem to justify this, I'm not sure why it's a big deal it seems a bit obvious to me. 4) it has to be a macroscopic variable and can be measured on macroscopic scale (its fluctuations diverge at the phase transition) * one has to measure it on scales >> lattice spacing so that it can be relatively UV insensitive. I have in mind averaging magnetic spins over mesoscopic scale for the O(N) model. I feel like order parameters are ultimately very subjective. There doesn't seem to be a "canonical" way to define it, but maybe I'm very naive. [/QUOTE]
Insert quotes…
Post reply
Forums
Physics
Atomic and Condensed Matter
Order parameter, symmetry breaking Landau style
Back
Top