1. What is the parameter that is discontinuous at a first order phase transition.
The free energy is discontinuous and hence there is an associated latent heat.
2. What is the infinitesimal magnetic work done on a sample when the applied field is increased by dH and the magnetisation of a configuration increases by dM. What is the work done on vacuum?
Work done on the sample is H.dM while that on vacuum is H.dH