**Background:** Scaling, Basic real space RG

The critical surface is formed of points in the phase space that have all relevant parameters = 0. Thus, any point on the critical surfact will move, under RG transformation towards the fixed point. It is because of this reason that we conclude that all points on the critical surface have the same critical exponents, although they may have different values of Tc. This also brings in the concept of universality, in that many different critical instances of the hamiltonian have the same exponents.

It seems to me that underlining this is an assumption that scaling does not change critical exponents. Can anyone provide a mathematically rigorous proof of this fact?

**Posted By:** Aakash Basu

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Hi, Critical exponents are physical, observable quantities, and by virtue of renormalization group invariance, have the sa me value for any chosen scale. This is, for example, not true of the beta function or for Green functions which will be modified according the scale or renormalization schemes chosen.

Sincerely A.Petermann.