When this happens, the system falls out of equilibrium and undergoes a kinetic glass transition.

[Fig4.eps]{}

The specific heat $C_P$ of experimental systems at constant pressure exhibits a downward step at the glass transition during cooling and a peak at slightly higher temperatures upon heating [@DeBolt76]. As can be seen in Figure \[fig:sphtCoolHeat\], in our warming up simulations, which are done at constant volume, the specific heat peak sharpens and moves toward higher temperatures compared to the cooling runs. This is consistent with what is seen in experiments. The hysteresis is consistent with the system falling out of equilibrium and getting stuck in a basin of the energy landscape.

[Fig5.eps]{}

As we mentioned in the introduction, some have suggested that the glass transition has an underlying second order phase transition [@Kirkpatrick89; @Sethna91; @Kivelson95; @Ernst91; @Dasgupta91; @Menon95]. Unlike typical second order phase transitions, there is no experimental evidence that the specific heat diverges at the glass transition. This is consistent with our simulations. In simulations one looks for a divergence by examining whether the quantity increases systematically with system size. In Figure \[fig:sphtSize\] we plot $C_V$ for systems with 64, 216, 512 and 1000 particles. As one can see, the specific 