Dynamic Susceptibility for Ising-Spin Clusters in Random Fields

Abstract

The dynamic susceptibility for a cluster of six coupled random field Ising spins in two different distributions, binary (BD) and Gaussian (GD), are calculated and exact results are obtained. The real and imaginary parts of the dynamic susceptibility display maxima when plotted versus temperature. These maxima can be described by an Arrhenius law. If the logarithm of the susceptibilities is plotted as a function of the logarithm of frequency and if the clusters are frustrated, then the real part displays a sequence of plateau regions and the imaginary part has a sequence of maxima in weak random fields. In the BD case of random field for large amplitudes there is only one plateau and one corresponding maximum as in ferromagnetic (FM) and paramagnetic (PM) cases. Our results confirm that any weak random field will turn out to destroy the ordered state and random field Ising‐spin clusters behave like Ising‐spin glasses.

Frequency dependence of the complex susceptibility for a spin-1 Ising model

“…The next simplest step in extending our analysis is to consider the same model in analogy to the work presented in Refs. [12][13][14][15] and investigate the relaxation behavior. In this way, a detailed study of the dynamic behavior of such a model would be very interesting.…”

“…Both the plateau and the maximum stay localized in the vicinity of offit 2 À1 with increasing T. But, the maximum in w 00 seems to be broader and its height increases with increasing kT/K while the plateau has a tendency to increase as in g M bg Q case. Similar results were also observed for the dynamic susceptibility of the SG systems [12], semimagnetic semiconductors with frustration [13], Ising-spin clusters in random fields [14], and Ising spins with AF bonds [15]. Existence of the gaps in the spectrum of the relaxation times obtained within the Glauber dynamics of these systems resulted in plateaus in w 0 and maxima in w 00 when w 0 and w 00 were plotted against o.…”

“…With increasing temperature, the two plateau regions would merge together to become only one and also the corresponding two maxima in the cluster [14]. The only difference relative to these theoretical systems is the number of diverging relaxation times as observed in the frequency-dependent susceptibility plots.…”

“…These phenomena were studied for the ferromagnetic (FM), paramagnetic (PM), and spin-glass (SG) systems (or frustrated spin clusters) based on Glauber dynamics [12]. The Glauber treatments of the above clusters were recently extended to semimagnetic semiconductors with frustration [13], Ising-spin clusters in random fields [14] and Ising spins with antiferromagnetic (AF) bonds [15].In this paper, we present the frequency-dependent behavior of the real and imaginary components of CS for the spin-1 Ising model with bilinear and biquadratic pair interactions. We use the method that combines the statistical equilibrium theory and irreversible thermodynamics.…”

Frequency Variation of the AC Order Parameter Susceptibility of the Metamagnetic Ising Model

“…Thus, in the metamagnetic phase, there exist two long and noticeably separated relaxation times for only | | ≫ | |. The gaps in the spectrum of the relaxation times are shown to affect both the reactive and the dissipative parts of the AC susceptibility spectra by making use of Glauber dynamics for various systems: spin-glass systems [23], frustrated semimagnetic semiconductors [24], Isingspin clusters in random fields [25], and Ising spins with AF bonds [26]. In these studies, the existence of the gaps in the spectrum of the relaxation times obtained within the Glauber dynamics which caused the real part of the frequency dependent susceptibility reveals a sequence of plateaus as a function of log , whereas the imaginary part displays a sequence of maxima.…”