Field-Theoretical Analysis of Critical and Coexistence Singularities at Critical End Points

Continuum models with critical end points are considered whose Hamiltonian ${\mathcal{H}}[\phi,\psi]$ depends on two densities $\phi$ and $\psi$. Field-theoretic methods are used to show the equivalence of the critical behavior on the critical line and at the critical end point and to give a systematic derivation of critical-end-point singularities like the thermal singularity $\sim|{t}|^{2-\alpha}$ of the spectator-phase boundary and the coexistence singularities $\sim |{t}|^{1-\alpha}$ or $\sim|{t}|^{\beta}$ of the secondary density $<\psi>$. The appearance of a discontinuity eigenexponent associated with the critical end point is confirmed, and the mechanism by which it arises in field theory is clarified.