  We study numerically the continuum limit corresponding to the non-trivial
fixed point of Dyson's hierarchical model. We discuss the possibility of using
the critical amplitudes as input parameters. We determine numerically the
leading and subleading critical amplitudes of the zero-momentum $2l$-point
functions in the symmetric phase up to l=10 for randomly chosen local measures.
In the infinite cutoff limit, the dimensionless renormalized coupling constants
are in very good approximation universal (independent of the choice of the
local measure). In addition, ratios of subleading amplitudes also appear to be
universal. If we neglect very small log-periodic corrections, the non-universal
features of the 2l-point functions appear to depend only the non-universal
features of the 2-point function. We infer that when 2l becomes large, the
dimensionless renormalized couplings grow as (2l)! despite the non-perturbative
nature of our calculation, while the universal ratios of subleading amplitudes
grow linearly.
