  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.
