In this old paper on Monte Carlo simulations of Lennard-Jones solid, specific heat behaviour (both $c_p$ and $c_v$) have been reported. As you can see from the picture below, both $c_p$ and $c_v$ goes to $3$ at $0K$. [The units in the plot are dimensionless reduced units defined based on the Lennard-Jones potential parameters]
Now, the heat capacity goes to zero, if the temperature approaches $0K$. Why this is not reflected here? Could this be due to the lack of quantum effects in the simulation?