Critical point shift in a fluid confined between opposing walls

TL;DR

This study investigates how gravity influences phase coexistence in a confined fluid or Ising magnet, revealing that gravity extends coexistence up to the critical temperature and detailing the scaling behavior near the critical point.

Contribution

It provides a detailed analysis of the critical point shift due to gravity in confined systems, including scaling laws and crossover behaviors, using density matrix renormalization techniques.

Findings

Gravity restores phase coexistence up to the bulk critical temperature.

The temperature shift scales as 1/L^{y_T}.

The gravitational constant scales as 1/L^{1+y_H} with system size.

Abstract

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$ geometry with opposing surface fields at the walls are studied by density matrix renormalization techniques. In particular we focus on the effect of gravity on the system, which is modeled by a bulk field whose strength varies linearly with the distance from the walls. It is well known that in the absence of gravity phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores phase coexistence up to the bulk critical temperature, in agreement with previous mean field results. A detailed study of the scaling to the critical point, as $L \to \infty$, is performed. The temperature shift scales as $1/L^{y_T}$, while the gravitational constant scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic exponents respectively. For weak surface fields and $L$ not too large, we also observe a regime where the gravitational constant scales as $1/L^{1+y_H - \Delta_1 y_T}$ ($\Delta_1$ is the surface gap exponent) with a crossover, for sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$.