Casimir Forces at Tricritical Points: Theory and Possible Experiments

TL;DR

This paper develops a theoretical framework for understanding Casimir forces at tricritical points using conformal invariance, analyzing various geometries and comparing forces in ternary mixtures, highlighting the dominance of tricritical Casimir forces with symmetry-breaking boundaries.

Contribution

It introduces a field-theoretical approach to tricritical Casimir forces, including boundary effects and diverse geometries, providing quantitative comparisons with other forces in mixtures.

Findings

Tricritical Casimir forces are stronger than critical Casimir forces.

Symmetry-breaking boundaries significantly enhance the Casimir force.

Tricritical Casimir forces can dominate van der Waals forces in mixtures.

Abstract

Using field-theoretical methods and exploiting conformal invariance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary transition). Besides the parallel-plate configuration, we also discuss the geometries of two separate spheres and a single sphere near a planar wall, which may serve as a model for colloidal particles immersed in a fluid. In the concrete case of ternary mixtures a quantitative comparison with critical Casimir and van der Waals forces shows that, especially with symmetry-breaking boundaries, the tricritical Casimir force is considerably stronger than the critical one and dominates also the competing van der Waals force.