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

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.