Phase transitions in nanosystems caused by interface motion: The Ising bi-pyramid with competing surface fields

TL;DR

This paper investigates phase transitions in a finite Ising bi-pyramid with competing surface fields, revealing a filling transition characterized by a discontinuous magnetization vanishing and diverging susceptibility, supported by simulations and phenomenological theory.

Contribution

It introduces a phenomenological Landau theory with size-dependent amplitudes to explain the filling transition in nanoscale systems, validated by Monte Carlo simulations.

Findings

Magnetization vanishes discontinuously at the filling transition.

Susceptibility diverges with a Curie-Weiss law near the transition.

Finite size scaling confirms the phenomenological theory.

Abstract

The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/- H_s is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bi-pyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L -> infinity) at the temperature T_f(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a susceptibility that diverges with a Curie-Weiss power law, when the transition is approached from either side. A Landau theory with size-dependent critical amplitudes is proposed to explain these observations, and confirmed by finite size scaling analysis of the simulation results. The extension of these results to other nanosystems (gas-liquid systems, binary mixtures, etc.) is briefly discussed.