  The phase-diagram of the two-dimensional Blume-Capel model with a random
crystal field is investigated within the framework of a real-space
renormalization group approximation. Our results suggest that, for any amount
of randomness, the model exhibits a line of Ising-like continuous transitions,
as in the pure model, but no first-order transition. At zero temperature the
transition is also continuous, but not in the same universality class as the
Ising model. In this limit, the attractor (in the renormalization group sense)
is the percolation fixed point of the site diluted spin-1/2 Ising model. The
results we found are in qualitative agreement with general predictions made by
Berker and Hui on the critical behaviour of random models.

Statistical Mechanics