I am confused about the (non)-existence of latent heat in the first order phase transition of the Ising model. Most textbooks talk about latent heat as a signature sign of a first order transition, but I was not able to find any discussion about it in relation to ferromagnetism (other than here).
The first order phase transition of the Ising model is effected by a change of sign in the applied magnetic field $h$ below the critical temperature $T_c$. This results in a discontinuous change in the magnetisation $m$. The latent heat $L$ associated with the transition depends on difference in entropy $\Delta s = s_+ - s_-$ between the up and down phases, and the temperature $T$ of the transition: $$ L = T \Delta s \, .$$ However, as the up and down phases are completely symmetric, they have the same entropy and therefore $$\Delta s = L = 0 \,.$$
This can also be seen from the Clausius-Clapeyron relation, $$\frac{dh}{dT} = \frac{L}{T \Delta m} \, . $$
From the phase diagram, it is obvious that $\frac{dh}{dT} = 0$, leading to $L = 0$.
I have a bunch of questions about all this:
- Is there really no latent heat?
- When using the Ising model to model a lattice gas, how does a nonzero latent heat emerge?
- Is there a general relationship between the slope of the coexistence line and the symmetry between two phases?
- Are there any other pedagogically relevant systems undergoing a first order transition with zero latent heat?