Fixed-magnetization Ising model with a slowly varying magnetic field

TL;DR

This paper analyzes the fixed-magnetization Ising model with a slowly varying magnetic field, focusing on magnetization profiles, interfacial phenomena, and conjectures about equilibrium crystal shapes under gravity.

Contribution

It characterizes magnetization profiles and interfacial phenomena in the fixed-magnetization Ising model with a varying magnetic field, including gravitational effects and conjectures on crystal shapes.

Findings

Characterized typical magnetization profiles in competing magnetic and bulk energy regimes.

Identified macroscopic profiles and interfacial phenomena in gravitational fields.

Proposed conjectures on equilibrium crystal shapes influenced by gravity.

Abstract

The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is a seen as a particular instance of an Ising model with a slowly varying magnetic field in the fixed magnetization ensemble. We first characterize the typical magnetization profiles in the regime in which the contribution of the magnetic field competes with the bulk energy term. We then discuss in more detail the particular case of a gravitational field and the arising interfacial phenomena. In particular, we identify the macroscopic profile and propose several conjectures concerning the interface appearing in the phase coexistence regime. The latter are supported by explicit computations in an effective model. Finally, we state some conjectures concerning equilibrium crystal shapes in the presence of a gravitational field, when the latter contributes to the energy only to surface order.