  X-ray magnetic critical scattering measurements and specific heat
measurements were performed on the perovskite iridate Sr$_3$Ir$_2$O$_7$. We
find that the magnetic interactions close to the N\'{e}el temperature $T_N$ =
283.4(2) K are three-dimensional. This contrasts with previous studies which
suggest two-dimensional behaviour like Sr$_2$IrO$_4$. Violation of the Harris
criterion ($d\nu>2$) means that weak disorder becomes relevant. This leads a
rounding of the antiferromagnetic phase transition at $T_N$, and modifies the
critical exponents relative to the clean system. Specifically, we determine
that the critical behaviour of Sr$_3$Ir$_2$O$_7$ is representative of the
diluted 3D Ising universality class.
