No or diffuse phase transition with temperature in one-dimensional Ising model?

TL;DR

This paper demonstrates that a diffuse phase transition with temperature occurs in the one-dimensional Ising model, challenging the traditional view of no phase transition in such systems, and provides a theoretical foundation for this phenomenon.

Contribution

It introduces an exact calculation of local spontaneous magnetization showing diffuse phase transition in 1D Ising model, filling a gap in theoretical understanding.

Findings

Diffuse phase transition occurs in 1D Ising model

Exact calculation of local spontaneous magnetization

Lays theoretical foundation for phase transitions in heterogeneous systems

Abstract

For nearly a century since Ising model was proposed in 1925, it is agreed that there is no phase transition with temperature in the one-dimensional based on no global spontaneous magnetization in whole temperature region. In this paper, the exact calculation of local spontaneous magnetization shows that a diffuse phase transition with temperature occurs in one-dimensional Ising model. In addition, although diffuse phase transition phenomenon is common in the systems of heterogeneous-components and grains etc., there is no accurate prediction of corresponding theoretical models so far, so the present works lay the theoretical foundation of this kind of phase transition.