Critical Casimir forces along the iso-fields

TL;DR

This paper investigates the behavior of critical Casimir forces in a 2D Ising model along paths with fixed nonzero bulk field, revealing significant temperature-dependent effects that differ from the zero-field case.

Contribution

It provides the first detailed numerical analysis of critical Casimir forces along iso-fields in a 2D Ising system, including force calculations for both strips and disc geometries.

Findings

Critical Casimir forces increase dramatically along iso-fields between coexistence and capillary condensation.

Force dependence on temperature differs qualitatively from the zero-field case.

Results may be relevant for understanding biomembrane heterogeneity near criticality.

Abstract

Using quasi-exact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h<>0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two discs. We find that varying the temperature along the iso-fields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.