Bulk singularities at critical end points: a field-theory analysis

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 $$ 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.Comment: Latex file; uses epj stylefiles svepj.clo and svjour.cls. Two eps files as figures included; uses texdraw to generate some figures Only some remarks added in last Section of this final versio

Interview with Jean Lamb

https://digitalcommons.providence.edu/psp470_2023/1005/thumbnail.jp

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 $$. 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.Comment: Latex2e file using elsart stylefile, no figures. submitted to Proceedings of Statphys Taipei-99, to be published in Physica

Development of targeted messages to promote smoking cessation among construction trade workers

Blue-collar workers, particularly those in the construction trades, are more likely to smoke and have less success in quitting when compared with white-collar workers. Little is known about health communication strategies that might influence this priority population. This article describes our formative work to develop targeted messages to increase participation in an existing smoking cessation program among construction workers. Using an iterative and sequential mixed-methods approach, we explored the culture, health attitudes and smoking behaviors of unionized construction workers. We used focus group and survey data to inform message development, and applied audience segmentation methods to identify potential subgroups. Among 144 current smokers, 65% reported wanting to quit smoking in the next 6 months and only 15% had heard of a union-sponsored smoking cessation program, despite widespread advertising. We tested 12 message concepts and 26 images with the target audience to evaluate perceived relevance and effectiveness. Participants responded most favorably to messages and images that emphasized family and work, although responses varied by audience segments based on age and parental status. This study is an important step towards integrating the culture of a high-risk group into targeted messages to increase participation in smoking cessation activities

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.Comment: 30 pages, 17 figure