  In agreement with the Harris criterion, asymptotic critical exponents of
three-dimensional (3d) Heisenberg-like magnets are not influenced by weak
quenched dilution of non-magnetic component. However, often in the experimental
studies of corresponding systems concentration- and temperature-dependent
exponents are found with values differing from those of the 3d Heisenberg
model.
  In our study, we use the field--theoretical renormalization group approach to
explain this observation and to calculate the effective critical exponents of
weakly diluted quenched Heisenberg-like magnet. Being non-universal, these
exponents change with distance to the critical point $T_c$ as observed
experimentally. In the asymptotic limit (at $T_c$) they equal to the critical
exponents of the pure 3d Heisenberg magnet as predicted by the Harris
criterion.
