  Using a simplified version of the RG transformation of Dyson's hierarchical
model, we show that one can calculate all the non-universal quantities entering
into the scaling laws by combining an expansion about the high-temperature
fixed point with a dual expansion about the critical point. The magnetic
susceptibility is expressed in terms of two dual quantities transforming
covariantly under the RG transformation and has a smooth limit in the
high-temperature limit. Using the analogy with hamiltonian systems, the
simplified example discussed here is similar to the anharmonic oscillator,
while more realistic examples can be tought of as coupled oscillators allowing
resonance phenomena.
