Field-theoretical analysis of singularities at critical end points

Continuum models with critical end points are considered whose Hamiltonian H[φ,ψ] depends on two densities φ and ψ. 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 ∼|t|2−α of the spectator-phase boundary and the coexistence singularities ∼|t|1−α or ∼|t|β of the secondary density 〈ψ〉. 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.