Specific heat of the classical ferromagnetic Heisenberg model I have simulated the classical ferromagnetic Heisenberg model on a cubic lattice using Monte Carlo and I get a finite specific heat near zero temperature. My understanding is that from the magnon theory, 
we should get a specific heat that behaves like ~ $T^{3/2}$. I have looked everywhere to find an answer to this question, but I have found none. I have read somewhere about the number of ground states not being necessarily the same for a finite system as for an infinite one, but I can't quite see 
the connection. Any help with this question will be much appreciated. The included figure is a sample of the results that I have obtained.

 A: This is essentially a result of the equipartition theorem where each degree of freedom contributes $k_B T/2$ to the energy. Given that the specific heat in this context is just ${\partial E}/{\partial T}$ then each degree of freedom contributes $k_B/2$ to the specific heat. For the classical model of lattice vibrations in solids this leads to the Dulong-Petit Law; i.e. a constant specific heat. 
For the classical Heisenberg model of interest the analogous harmonic modes are the spin waves about the ferromagnetically ordered state. Since there are as many spin wave modes as sites, and each contributes two degrees of freedom (roughly: the two directions transverse to the ordered moment) you would expect an energy per site from these modes of $E = 2 (k_B T/2) = k_BT$ and thus a contribution to the specific heat of $C \sim k_B$. In more natural units this would be $C \sim 1$, as you find in your simulations. This should only occur at low temperature (well below the ordering transition) where this spin-waves are well defined.
In regard to the $C \sim T^{3/2}$ law for magnons; this is a result of quantum mechanics, in the same way the low temperature Debye specific heat, $C \sim T^3$, is for phonons. To find this result one needs both the ferromagnetic dispersion that goes as $\omega \sim k^2$ at long wave-lengths, as well as Bose statistics for the magnons.
