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

TL;DR

This paper uses field-theoretic methods to analyze critical and coexistence singularities at critical end points in continuum models with two densities, clarifying their behavior and singularities.

Contribution

It systematically derives critical-end-point singularities and clarifies the emergence of a discontinuity eigenexponent using field theory.

Findings

Equivalence of critical behavior on the critical line and at the critical end point.

Derivation of thermal and coexistence singularities in the model.

Confirmation and explanation of the discontinuity eigenexponent.

Abstract

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.