Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

TL;DR

This paper investigates how gravity and confinement influence phase diagrams of the 2D Ising model, revealing that gravity extends phase coexistence to the critical temperature, with detailed scaling and magnetization profile analyses.

Contribution

It introduces a density matrix renormalization approach to analyze the effects of gravity and confinement on phase equilibria in the 2D Ising model, including scaling exponents and magnetization profiles.

Findings

Gravity restores phase coexistence up to the critical temperature.

Finite size scaling exponents are calculated for temperature and gravitational field directions.

Magnetization profiles match simple interface Hamiltonian predictions.

Abstract

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.