Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations

TL;DR

This paper establishes a quantitative link between critical Casimir forces and percolation clusters in the Ising model, introduces a new Monte Carlo method for force computation, and investigates non-additivity effects.

Contribution

It presents a novel Monte Carlo approach to compute critical Casimir forces using percolation cluster correlations in the Ising model, and explores non-additivity of these forces.

Findings

Validated the new Monte Carlo method for 2D Ising model

Quantified non-additive contributions to three-particle interactions

Linked critical Casimir forces to percolation cluster fluctuations

Abstract

Casimir forces in a critical media are produced by spatial suppression of order parameter fluctuations. In this paper we address the question how fluctuations of a critical media relates the magnitude of critical Casimir interactions. Namely, for the Ising model we express the potential of critical Casimir interactions in terms of Fortuin-Kasteleyn site-bond correlated percolation clusters. These clusters are quantitative representation of fluctuations in the media. New Monte Carlo method for the computation of the Casimir force potential which is based on this relation is proposed. We verify this method by computation of Casimir interactions between two disks for 2D Ising model. The new method is also applied to the investigation of non-additivity of the critical Casimir potential. The non-additive contribution to three-particles interaction is computed as a function of the temperature.