Question

What should I think of a diverging beta function (in Renormalisation Group flow)?

Answer 1

HOPE THIS MAY HELP U

Answer 2

I am looking into the RG flow of the O(N) model. I have included a 4-point coupling that contains two spatial derivatives. When the field expectation value ρ0 is very small, one of the new couplings decouples from all the other couplings. I get the following beta functions

βnew=−4λnew(8π+λnew)ρ0,

βρ0=0.

If this is initiated with −8π<λnew<0, the flow equation

∂tλnew=βnew,

decreases λnew until it becomes equal to −8π and the RG flow stops.

I find this very strange and do no know what do think about it. The only thing that I can think of is that my approximation scheme really bad and that I should not trust this part of my calculation. What do you think?

quantum-field-theory