Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-02-05
Eur.Phys.J. B21 (2001) 567-587
Physics
Condensed Matter
Statistical Mechanics
Latex file; uses epj stylefiles svepj.clo and svjour.cls. Two eps files as figures included; uses texdraw to generate some fig
Scientific paper
10.1007/PL00011126
A class of continuum models with a critical end point is considered whose Hamiltonian ${\mathcal{H}}[\phi,\psi]$ involves two densities: a primary order-parameter field, $\phi$, and a secondary (noncritical) one, $\psi$. 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 $\sim|{t}|^{2-\alpha}$ of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity $\sim |{t}|^{1-\alpha}$ or $\sim|{t}|^{\beta}$ of the secondary density $<\psi>$ 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 ${\mathcal P}_{\mathrm{CEP}}^*$ and ${\mathcal P}_{\lambda}^*$ translates into field theory. The critical RG eigenexponents of ${\mathcal P}_{\mathrm{CEP}}^*$ and ${\mathcal P}_{\lambda}^*$ are shown to match. ${\mathcal P}_{\mathrm{CEP}}^*$ is demonstrated to have a discontinuity eigenperturbation (with eigenvalue $y=d$), tangent to the unstable trajectory that emanates from ${\mathcal P}_{\mathrm{CEP}}^*$ and leads to ${\mathcal P}_{\lambda}^*$. 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.
Diehl H. W.
Smock M.
No associations
LandOfFree
Bulk singularities at critical end points: a field-theory analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bulk singularities at critical end points: a field-theory analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bulk singularities at critical end points: a field-theory analysis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-104623