Crossover of Critical Casimir forces between different surface universality classes

TL;DR

This paper investigates the behavior of critical Casimir forces in confined systems near phase transitions, focusing on the crossover between different surface universality classes, using mean field theory and Monte Carlo simulations.

Contribution

It provides a detailed analysis of the crossover regime of critical Casimir forces between different surface universality classes, including mapping of scaling functions and sign change behavior.

Findings

Critical Casimir force exhibits multiple extrema and sign changes with temperature.

Scaling functions can be mapped onto the normal fixed point for finite surface fields.

Monte Carlo simulations confirm the mean field theory trends.

Abstract

In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean field theory. Within our approach, the scaling functions of the critical Casimir force and of the order parameter profile for finite surface fields can be mapped by rescaling, except for a narrow crossover regime, onto the corresponding scaling function of the so-called normal fixed point of strong surface fields. In the crossover regime, the critical Casimir force as function of temperature exhibits more than one extremum and for certain ranges of surface field strengths it changes sign twice upon varying temperature. Monte Carlo simulation data obtained for a three-dimensional Ising film show similar trends. The sign of the critical Casimir force can be inferred from the comparison of the order parameter profiles in the film and in the semi-infinite geometry.