We identify conditions for the presence of negative specific heat in non-relativistic self-gravitating systems and similar systems of attracting particles .

The method used , is to analyse the Virial theorem and two soluble models of systems of attracting particles , and to map the sign of the specific heat for different combinations of the number of spatial dimensions of the system , D ( \geq 2 ) , and the exponent , \nu ( \neq 0 ) , in the force potential , \phi = Cr ^ { \nu } .
Negative specific heat in such systems is found to be present exactly for \nu = -1 , at least for D \geq 3 .
For many combinations of D and \nu representing long-range forces , the specific heat is positive or zero , for both models and the Virial theorem .
Hence negative specific heat is not caused by long-range forces as such .
We also find that negative specific heat appears when \nu is negative , and there is no singular point in a certain density distribution .
A possible mechanism behind this is suggested .