The van Hemmen model in the presence of a random field

Abstract

The van Hemmen model with a random field is studied to analyze the tricritical behavior in the Ising spin glass phase. The free energy and phase diagram (T versus H and T versus J o /J, where H is the root mean square deviation of the magnetic field, J o and J are the ferromagnetic and root mean square deviation exchange, respectively) are calculated for the model with discrete (or bimodal) and Gaussian distributions. For the case of the bimodal probability distribution (random field and exchange), we have the presence of three ordered phases, namely: spin glass (SG), mixed (∏) and ferromagnetic (F). The root mean square deviation of the random field H destroys the spin glass and mixed phases. The mixed phase doesn't appear with Gaussian distribution. In the plane T versus H, we analyze the tricritical behavior for the case of the bimodal distribution, and we compare it with the results obtained by using the Gaussian distribution that presents only second-order phase transition.

Unfolding of phases and multicritical points in the classical anisotropic van Hemmen spin glass model with random field

“…Next, we briefly discuss the contribution of our work as compared with previous studies of magnetic models with RF. In fact, the results obtained in the Blume-Capel model [19] or in the Ising van Hemmen model [16] both with RF can be considered limit situations of our model. The first case corresponds to the situation where J 0 >> J while the second one corresponds to D → −∞.…”

“…For instance, It is well known that D > 0 tends to destroy any magnetic long range order by favoring states S = 0. In its turn, previous results on the Ising van Hemmen model with RF [16] show that the RF tends to suppress the SG phase. Therefore, it is quite clear that neither the RF nor the D acting alone can produce the unfolding of phase obtained in our work.…”

Finite-Temperature Avalanches in 2D Disordered Ising Models

“…Most studies in this context make some further simplifying assumptions. For example, the analysis is performed only at T = 0, or fully connected spin networks (mean-field model) are considered [17,[20][21][22]. When short range interactions are taken into account, a typical model is the ±J model, which has antiferromagnetic bonds −J with probability p, and ferromagnetic bonds +J with probability 1 − p. On a square lattice, when p exceeds a critical value p c , it is expected to observe a transition from a ferromagnetic to a spin-glass phase [16,21].…”

“…The behaviour of the system varies significantly when the disorder parameter R is increased above a critical value. In the disordered regime the ferromagnetic phase becomes unstable, the free energy exhibits many metastable states and a glassy-like phase emerges [20,21]. We located the ferro-glass transition by creating N r = 100 different replicas of a system with specific values of R and J , and running a Monte-Carlo simulation at each different temperature, to compute the average magnetization.…”

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

“…11,24,[59][60][61][62] The study of this generalized Mattis model is very interesting not only in understanding the behavior of those relatively realistic spin glass models but also in the context of the models of neural networks that is known as the Hopfield spin glass. 63…”