Devil's staircase in kinetically limited growth of Ising model

TL;DR

This paper investigates how kinetically limited growth processes in an Ising model lead to complex layered structures characterized by a devil's staircase, revealing the intricate relationship between growth kinetics and equilibrium phases.

Contribution

It demonstrates that growth kinetics can produce a devil's staircase structure, connecting non-equilibrium growth patterns to equilibrium phase diagrams in the Ising model.

Findings

Growth structures tend to the equilibrium ground state via a devil's staircase.

Layered structures are determined by growth kinetics rather than thermodynamic ground states.

Complex intermediate phases are traversed during the growth process.

Abstract

The devil's staircase is a term used to describe surface or an equilibrium phase diagram in which various ordered facets or phases are infinitely closely packed as a function of some model parameter. A classic example is a 1-D Ising model [bak] wherein long-range and short range forces compete, and the periodicity of the gaps between minority species covers all rational values. In many physical cases, crystal growth proceeds by adding surface layers which have the lowest energy, but are then frozen in place. The emerging layered structure is not the thermodynamic ground state, but is uniquely defined by the growth kinetics. It is shown that for such a system, the grown structure tends to the equilibrium ground state via a devil's staircase traversing an infinity of intermediate phases. It would be extremely difficult to deduce the simple growth law based on measurement made on such an grown structure.