No or Diffuse Phase-Transition With Temperature in One-dimensional Ising Model?

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 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.

Activity and steady‐state kinetics of one‐dimensional kinetic Ising model

“…The methods to obtain the partition function and to apply it to obtain the most important statistical properties of the present model are standard and can be found in many textbooks and articles. The procedures presented in this Subsection follow the text of K. Huang [17] and the book chapter by H. W. Huang and W. A. Seitz. [18] The partition function of this system can be written as…”