Bobhawke
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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 doesn't 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?
[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 doesn't 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?