https://doi.org/10.1007/PL00011126
Bulk singularities at critical end points: a field-theory analysis
Fachbereich Physik, Universität Essen,
45117 Essen, Germany
Corresponding author: a phy300@theo-phys.uni-essen.de
Received:
18
January
2001
Published online: 15 June 2001
A class of continuum models with a critical end point is considered
whose Hamiltonian 
involves two densities:
a primary order-parameter field, ϕ, and a secondary
(noncritical) one, ψ. Field-theoretic methods (renormalization group
results in conjunction with functional methods) are used to give a
systematic derivation of singularities occurring at
critical end points. Specifically, the thermal
singularity 
of the first-order line on which
the disordered or ordered
phase coexists with the noncritical spectator phase,
and the coexistence singularity 
or
of the secondary density 
are derived.
It is clarified how the
renormalization group (RG) scenario found in position-space RG
calculations, in which the critical end point and the critical line are
mapped onto two separate fixed points 
and 
, translates into field theory.
The critical RG eigenexponents of
and are shown to
match. is demonstrated
to have a discontinuity eigenperturbation (with
eigenvalue y=d), tangent to the unstable trajectory that emanates
from and leads to .
The nature and origin
of this eigenperturbation as well as the role redundant operators
play are elucidated. The results validate that
the critical behavior at the end point is the same as on the critical line.
PACS: 64.60.Fr – Equilibrium properties near critical points, critical exponents / 05.70.Jk – Critical point phenomena / 68.35.Rh – Phase transitions and critical phenomena / 11.10.Hi – Renormalization group evolution of parameters
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
