Phase transitions in one dimension: are they all driven by domain walls?

TL;DR

This paper critically examines two one-dimensional models with phase transitions, showing that domain wall configurations become entropically stable at critical points, suggesting a potential criterion for phase transitions in 1D systems.

Contribution

It proposes that entropic stability of domain walls may serve as a criterion for phase transitions in one-dimensional systems, based on analysis of two known models.

Findings

Domain walls become entropically stable at critical temperature

Both models exhibit phase transitions linked to domain wall stability

Suggests a possible universal criterion for 1D phase transitions

Abstract

Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B) the ferromagnetic, spin 1/2 Ising model with long-range pair interactions varying as the inverse square of the distance between pairs. In both cases it can be shown that the domain wall configurations become entropically stable at, or very near, the critical temperature. This might provide a "positive" criterion for the occurrence of a phase transition in one-dimensional systems.