  We present a number of analytical results which should guide the
interpretation of lattice data in theories with an infra-red fixed point (IRFP)
deformed by a mass term deltaL = - m \bar qq. From renormalization group (RG)
arguments we obtain the leading scaling exponent, F ~ m^(eta_F), for all decay
constants of the lowest lying states other than the ones affected by the chiral
anomaly and the tensor ones. These scaling relations provide a clear cut way to
distinguish a theory with an IRFP from a confining theory with heavy fermions.
Moreover, we present a derivation relating the scaling of <\bar qq> \sim
m^(eta_qq) to the scaling of the density of eigenvalues of the massless Dirac
operator rho(lambda) ~ lambda^(eta_qq) RG arguments yield eta_qq =
(3-gamma*)/(1+\gamma*)$ as a function of the mass anomalous dimension gamma* at
the IRFP. The arguments can be generalized to other condensates such as <G^2> ~
m^(4/(1+gamma*)). We describe a heuristic derivation of the result on the
condensates, which provides interesting connections between different
approaches. Our results are compared with existing data from numerical studies
of SU(2) with two adjoint Dirac fermions.
