  We show that an interaction decaying as a stretched exponential function of
the distance, $J(l)\sim e^{-cl^a}$, is able to alter the universality class of
short-range systems having an infinite-disorder critical point. To do so, we
study the low-energy properties of the random transverse-field Ising chain with
the above form of interaction by a strong-disorder renormalization group (SDRG)
approach. We obtain that the critical behavior of the model is controlled by
infinite-disorder fixed points different from that of the short-range one if
$0<a<1/2$. In this range, the critical exponents calculated analytically by a
simplified SDRG scheme are found to vary with $a$, while, for $a>1/2$, the
model belongs to the same universality class as its short-range variant. The
entanglement entropy of a block of size $L$ increases logarithmically with $L$
in the critical point but, as opposed to the short-range model, the prefactor
is disorder-dependent in the range $0<a<1/2$. Numerical results obtained by an
improved SDRG scheme are found to be in agreement with the analytical
predictions. The same fixed points are expected to describe the critical
behavior of, among others, the random contact process with stretched
exponentially decaying activation rates.
