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Analogue of Callan-Symanzik equation for Ising model

  1. Mar 4, 2009 #1
    When I studied renormalisation for the Ising model the procedure was to sum over every second spin and then find a new coupling which produced the same physics. This leads to a relation between the coupling at different scales of the form

    [itex] K(2s)=f(K(s)) [/itex]

    Where K is the coupling, s is the scale that it is measured at, and f is the function that relates them.

    This tells you the renormalisation group flow, but it doesnt tell you what the coupling is at all scales, just at multiples of 2 of your original scale.

    My question is this: would it be possible to form a differential equation for the Ising model (or other statistical system), analagous to the Callan-Symanzik equation for QFT, which tells you how the copuling changes with scale for all scales?
  2. jcsd
  3. Mar 5, 2009 #2
    Do everything in Fourier space. Integrate out thin shells in momenta, then rescale to restore contrast.
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