Interfacial Structural Changes and Singularities in Non-Planar Geometries

TL;DR

This paper investigates how non-planar geometries affect phase coexistence, interface structure, and critical phenomena in a thin-film Ising magnet, revealing unexpected non-linear effects and multiple critical exponents.

Contribution

It demonstrates the impact of non-planar walls on interface singularities and critical behavior, introducing new non-thermodynamic singularities and contrasting critical exponents with planar cases.

Findings

Identification of four non-thermodynamic singularities affecting interface shape

At the finite-size critical point, two distinct critical exponents are observed

Analogies drawn with chaotic dynamics in non-linear oscillators

Abstract

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics.