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In this paper we investigate the behaviour of the specific heat around thecritical point of the Ising model in dimension 5 to 7. We find a specific heatdiscontinuity, like that for the mean field Ising model, and provide estimatesfor the left and right hand limits of the specific heat at the critical point.We also estimate the singular exponents, describing how the specific heatapproaches those limits. Additionally, we make a smaller scale investigation ofthe same properties in dimension 6 and 7, and provide strongly improvedestimates for the critical termperature $K_c$ in $d=5,6,7$ which bring the bestMC-estimate closer to those obtained by long high temperature series expanions.

The discontinuity of the specific heat for the 5D Ising model