# Manipulation and amplification of the Casimir force through surface fields using helicity

## TL;DR

This paper investigates how surface fields inducing helicity can manipulate the Casimir force in $O(n)$ systems, revealing conditions for force amplification, sign change, and dependence on system parameters through exact and numerical methods.

## Contribution

It provides the first exact and numerical analysis of the Casimir force in $O(n)$ models with helicity-inducing surface fields, demonstrating force control via surface modulation.

## Key findings

- Casimir force scales as $L^{-2}$ in certain temperature ranges
- Force can be attractive or repulsive depending on parameters
- Results align with finite size scaling principles

## Abstract

We present both exact and numerical results for the behavior of the Casimir force in $O(n)$ systems with a finite extension in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems the Casimir force in certain temperature ranges is of the order of $L^{-2}$, both above and below the critical temperature, $T_c$, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one dimensional $XY$ and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle and the three dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean field version of the three dimensional $O(2)$ model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite size scaling.