Critical-exponent renormalization, first-order transitions and demagnetizing effects for Schofield's linear model

The critical behaviour of a reference system with short-range interactions under small perturbations is investigated in detail for the special case of two (relevant) thermodynamic fields h1 and h2. As reference system we choose Schofield's linear model and we consider perturbations of the type ∏1m12 + ∏2m22, where m1 and m2 are thermodynamic variables conjugate to the fields h1 and h2. Explicit estimates are given for the four different regimes of critical-exponent renormalization, in the special case that ∏1>0, ∏2>0. In general there can be first- and second-order transitions in the neighbourhood of the critical point of the reference system between two “normal” phases and a “demagnetizing” phase. The various types of phase diagrams are presented.