  We briefly review the Ising model with uncorrelated, quenched random-site or
random-bond disorder, which has been controversial in both two and four
dimensions. In these dimensions, the leading exponent alpha, which
characterizes the specific-heat critical behaviour, vanishes and no Harris
prediction for the consequences of quenched disorder can be made. In the
two-dimensional case, the controversy is between the strong universality
hypothesis which maintains that the leading critical exponents are the same as
in the pure case and the weak universality hypothesis, which favours
dilution-dependent leading critical exponents. Here the random-site version of
the model is subject to a finite-size scaling analysis, paying special
attention to the implications for multiplicative logarithmic corrections. The
analysis is fully supportive of the scaling relations for logarithmic
corrections and of the strong scaling hypothesis in the 2D case. In the
four-dimensional case unusual corrections to scaling characterize the model,
and the precise nature of these corrections has been debated. Progress made in
determining the correct 4D scenario is outlined.
