# Analogue of Callan-Symanzik equation for Ising model

1. Mar 4, 2009

### Bobhawke

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

$K(2s)=f(K(s))$

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. Mar 5, 2009

### genneth

Do everything in Fourier space. Integrate out thin shells in momenta, then rescale to restore contrast.