Geometrical Phase Transition on WO$_3$ Surface

TL;DR

This study investigates a geometrical phase transition on WO$_3$ surfaces using percolation theory, revealing a critical height level where an infinite island forms, characterized by critical exponents consistent with long-range correlated percolation.

Contribution

The paper introduces a novel application of percolation theory to analyze topographical data of WO$_3$ surfaces, identifying a geometrical phase transition and calculating associated critical exponents.

Findings

Identification of a critical height level $oldsymbol{ ext{δ}_c}$ for phase transition.

Determination of critical exponents consistent with long-range correlated percolation.

Potential for generalizing the method to classify rough surface models.

Abstract

A topographical study on an ensemble of height profiles obtained from atomic force microscopy techniques on various independently grown samples of tungsten oxide WO$_3$ is presented by using ideas from percolation theory. We find that a continuous 'geometrical' phase transition occurs at a certain critical level-height $\delta_c$ below which an infinite island appears. By using the finite-size scaling analysis of three independent percolation observables i.e., percolation probability, percolation strength and the mean island-size, we compute some critical exponents which characterize the transition. Our results are compatible with those of long-range correlated percolation. This method can be generalized to a topographical classification of rough surface models.