Specific heat of bosons in a lattice

We present a theoretical study of specific heat of bosons (Cv) in a simple cubic lattice. We have studied the non-interacting bosons and the Tonks gas. For both cases, the Cv above the Bose condensation temperature shows considerable temperature dependence compared to that of free bosons. For Tonks gas, we find that the low-temperature specific heat increases as the system gets closer to the Mott transition.