Constraints, phase transitions and critical indices

The notion of first order phase transitions is examined for systems under external constraints. It is emphasized that only discontinuities with respect to “natural” variables (additive extensive variables and their conjugate internal forces) should be regarded as first order transitions. The Baker-Essam model is accordingly reviewed, and it is shown that the transition is always of the second order. Fisher's conjecture about renormalization is shown to be correct also for this model.