  This work analyzes a percolation model on the diamond hierarchical lattice
(DHL), where the percolation transition is retarded by the inclusion of a
probability of erasing specific connected structures. It has been inspired by
the recent interest on the existence of other universality classes of
percolation models. The exact scale invariance and renormalization properties
of DHL leads to recurrence maps, from which analytical expressions for the
critical exponents and precise numerical results in the limit of very large
lattices can be derived. The critical exponents $\nu$ and $\beta$ of the
investigated model vary continuously as the erasing probability changes. An
adequate choice of the erasing probability leads to the result $\nu=\infty$,
like in some phase transitions involving vortex formation. The percolation
transition is continuous, with $\beta>0$, but $\beta$ can be as small as
desired. The modified percolation model turns out to be equivalent to the
$Q\rightarrow1$ limit of a Potts model with specific long range interactions on
the same lattice.

Statistical Mechanics