Effective forces induced by fluctuating interface: exact results

TL;DR

This paper derives exact formulas for fluctuation-induced forces between interfaces in different dimensions, revealing decay behaviors of 1/r in 2D and 1/(r log r) in 3D, advancing understanding of interfacial phenomena.

Contribution

It provides the first exact derivations of fluctuation-induced forces for interfaces in both 2D and 3D systems, using transfer matrix and bosonization methods.

Findings

In 2D, the force decays as 1/r with distance.

In 3D, the force decays as 1/(r log r).

Exact solutions confirm the attractive nature of the forces.

Abstract

We present exact derivations of the effective capillary wave fluctuation induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance r. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as 1/r for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the bosonization analysis of the equivalent XXZ Heisenberg quantum chain. The exact result gives the attractive force which decays asymptotically as 1/(r\log r).