Long-range Coulomb forces and the behavior of the chemical potential of electrons in metals at a second-order phase transition

We give a general thermodynamic analysis of the behavior of the chemical potential of electrons in metals at a second-order phase transition, including in our analysis the effect of long-range Coulomb forces. It is shown that this chemical potential can have a kink at T_c, both for fixed sample volume and fixed external pressure. The Coulomb term transfers the changes in chemical potential of the electrons into an experimentally observable shift of the surface potential if the sample is electrically connected to a ground potential.