Critical exponents for O(n) models
We consider the critical behaviour of long-range O(n) models
for n greater than or equal to 0. For n=1,2,3,... these
are phi^4 spin models. For n=0 it is the weakly self-avoiding walk.
We prove existence of critical exponents for the susceptibility
and the specific heat, below the upper critical dimension.
This is a rigorous version of the epsilon expansion in physics.
The proof is based on a rigorous renormalisation group method
developed in previous work with Bauerschmidt and Brydges.