Universality in the point discretization method for calculating Casimir interactions with classical Gaussian fields

Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS F-75205 Paris, France, EU

Received: 10 July 2012
Accepted: 19 October 2012

Abstract

We study how universality arises when computing Casimir interactions between arbitrary bodies by discretizing their boundaries into pointlike constraints viewed as pointlike inclusions. Introducing ad hoc cutoff and regularization for the field's correlation function, we find that universality arises when i) the separation δ between the pointlike inclusions is less than the cutoff Λ⁻¹, and ii) the bodies are much larger than the cutoff. A sharp transition from discrete to continuous boundaries occurs at δ = π/Λ in the thermodynamic limit for rods at large separation. We illustrate our findings in two dimensions with rodlike bodies and more complex bodies shaped as moons.