# Why is specific heat not zero at absolute zero?

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?

You are correct that this is due to not including quantum effects. Ref 1 in your figure is the paper cited below. In this paper, they explicitly mention that $$C_v$$ calculated using the cell-cluster method is in good agreement only for sufficiently high reduced-temperatures. From section IV of this paper:

...the calculation is in acceptable agreement with experiment, except for low reduced temperatures, where quantum- mechanical effects become significant.

As further illustration, this paper has a similar plot of the cell-cluster results, but instead of comparing against Monte Carlo, they compare with experimental results for xenon.

As you can see, the experimental results approach zero as they should. The cell-cluster results do at least satisfy Mayer's Relation, which says $$C_P-C_V=0$$ at $$T=\pu{0K}$$.

1. K. Westera and E. R. Cowley Phys. Rev. B 11, 4008 (1975) DOI: 10.1103/PhysRevB.11.4008
• pardon my ignorance, but do you know why it goes to 3, the specific heat using cell-cluster method? Because I have seen some MD simulation paper on the same topic (c_p/c_v of LJ solid), and specific heat always goes to 3 reduced unit at low (Zero) temperature. Dec 31 '20 at 2:07
• @Magic_Number I'm not exactly certain. I know 3 (Nk) shows up in a lot of models of heat capacity (the Dulong-Petit Law, Einstein solid), but I haven't seen any model where the zero temperature limit specifically converges to 3.
– Tyberius
Dec 31 '20 at 2:40