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 letter, 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 small-sizes 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.