Scaling of solvation force in 2D Ising strip

TL;DR

This paper calculates the solvation force in a 2D Ising strip using exact transfer matrix methods, analyzing symmetric and antisymmetric surface field cases and proposing a scaling function for its behavior.

Contribution

It provides an exact analysis of the solvation force in a 2D Ising strip for different surface field configurations and introduces a scaling function for its dependence on key parameters.

Findings

Solvation force is always attractive in symmetric case.

In antisymmetric case, force is repulsive at high T and attractive at low T.

Force sign change occurs near the critical wetting temperature.

Abstract

The solvation force for the 2D Ising strip is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical surface fields, and the antisymmetric case to exactly opposite surface fields. In the symmetric case the solvation force is always negative (attractive) while in the antisymmetric case the solvation force is positive (repulsive) at high temperatures and negative at low temperatures. It changes sign close to the critical wetting temperature characterizing the semi--infinite system. The properties of the solvation force are discussed and the scaling function describing its dependence on temperature, surface field, and strip's width is proposed.