Testing renormalization group theory at the critical dimension in ${\mathrm{LiHoF}}_4$

We have performed high-precision specific heat measurements on the Ising dipolar magnet ${\mathrm{LiHoF}}_4$ in the critical regime (reduced temperature $|t|\lesssim 0.02).$ Combining these results with existing magnetization M and susceptibility $\chi$ data, we test renormalization group predictions at the critical dimension. In particular, the nontrivial prediction that $t^2\chi C_P{T}_C{/M}^2=\frac{1}{3}$ is well verified.