Random Impurities as the Cause of Smooth Specific Heats Near the Critical Temperature

We present a modification of the two-dimensional Ising model which incorporates random impurities. The specific heat of this model is infinitely differentiable even at the critical temperature where it possesses an essential singularity. We find this specific heat to be in perfect quantitative agreement with the smooth peak recently observed by van der Hoeven, Teaney, and Moruzzi for $T\gtrsim T_c$ in the specific heat of EuS.