Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference between corelation function and corelation lenght

  1. Aug 14, 2012 #1
    For example if we look Ising model correlation function is
    [tex]\langle S_iS_{i+j}\rangle[/tex]
    So we can see that if we took into acount just nearest neighbours interraction we also will see that some [tex]i+j[/tex]-th spin feels i-th spin. So there is some correlation between them.
    Am I right? This is correlation function. And what is correlation lenght?

    Is it lenght between
    [itex]\uparrow\uparrow\uparrow\uparrow\downarrow\downarrow[/itex]
    the biggest number of align spins?
     
  2. jcsd
  3. Aug 14, 2012 #2
    If I watch some spin system, for example Ising model or something, what is for me there correlation lenght? Can you explain this to me?
     
  4. Aug 15, 2012 #3

    atyy

    User Avatar
    Science Advisor

    I'm not sure if the usage in condensed matter is the same, but usually the correlation function is more general. When the correlation function is exponential, exp(-x/L), then L is the correlation length. If the correlation function is a power law, x^n, then the correlation length is not defined (or "infinite", eg. http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/060418_Harvard.pdf says "power-law phase with infinite correlation length").
     
  5. Aug 16, 2012 #4
    Yes, I think it's the same. Just in condensed matter I have maybe

    [tex]\Gamma=exp(-\frac{an}{L})[/tex]

    where [tex]a[/tex] is distance between nearest neighbours. I don't understand very well that if I see phase transition in some point then correlation lenght there is pretty large. So [tex]\Gamma[/tex] goes to zero. Right?

    And where I can have polynomial dependence? In ordered phase. Can someone explain me that?
     
  6. Aug 16, 2012 #5

    atyy

    User Avatar
    Science Advisor

    The divergence of the correlation length only occurs at some phase transitions, eg. at the critical point , which is where the boundary between liquid and gas disappears. Kardar has some notes on this. He writes the correlation function as a power law multiplying an exponential (Eq II.46). The correlation function is approximately a power law only for distances less than the correlation length (Eq II.49). As the critical point is approached, the correlation length diverges, and so the correlation function is close to a power law over very large distances (see his comments before Eq II.52).
    http://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2008/lecture-notes/lec2.pdf [Broken]
    http://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2008/lecture-notes/lec3.pdf [Broken]
    http://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2008/lecture-notes/lec4.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Difference between corelation function and corelation lenght
  1. Difference between (Replies: 2)

  2. Corelation function (Replies: 3)

  3. Differences between (Replies: 2)

Loading...