Crossover between a short-range and a long-range Ising model

Abstract

Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, we generally expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has nonzero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a finite-size scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.

Effect of intermolecular interactions on the nucleation, growth, and propagation of like-spin domains in spin-crossover materials

“…However, a gradual transition described by a simple Boltzmann distribution between the two states * ahmed@tcl.t.u-tokyo.ac.jp † kbo@physique.uvsq.fr is generally obtained in highly diluted crystals, considered as noncooperative systems [15]. Several research works have focused on the contribution of the elastic interactions from the theoretical [16][17][18][19][20][21][22][23][24][25][26] and experimental points of view [27,28]. In fact, theoretical models devoted to the investigation of the spin transition simulate quite well the experimental phase diagrams; however, some limitations emerge when the spatiotemporal aspects of the transition are considered.…”

Properties of the low-spin high-spin interface during the relaxation of spin-crossover materials, investigated through an electro-elastic model

“…14,15 This pressure effectively acts on all molecules of the crystal (independent of distances) with the same strength. The contribution of the elastic interactions has been studied in detail both theoretically [16][17][18][19][20][21][22][23][24][25][26] and experimentally by measuring the elastic constants by Brillouin spectroscopy 27 and the strain tensors through temperature dependent x-rays diffraction. 28 From the general point of view, the present problem is similar to that of statistical mechanics of miscibility and superstructure formation of solids binary alloys which was studied in the past in the frame of lattice-gas models.…”

“…However, the model limitations are quite obvious: each lattice site interacts with a fixed neighbor through a fixed interaction constant and the interplay between the elastic distortions and the spin composition cannot be properly modeled. Recent works [18][19][20][21][22][23][24][25][26] pointed out the importance of the spin-lattice interaction which can even change the nature of the phase transition. Here, we present an approach aiming to investigate the physics of the HS:LS interface in spin crossover solids.…”

Adatom pair distribution up to half coverage: O-Pd(100)

“…The lack of long range order predicted by the current elastic model corresponds with an Ising model including long range interactions [23].…”