Dynamics of Ising spins with antiferromagnetic bonds on a triangular lattice

Abstract

Six-coupled Ising spins on a triangular lattice with antiferromagnetic (AF) nearest neighbour and ferromagnetic (F) next-nearest neighbour interactions are investigated by Glauber dynamics. The system is fully frustrated and has seven non-trivial local energy minima in both clusters. The ground state has four degenerate states with energy -6. These states are separated by the energy barrier ∆E = 4.0 to invert spins in the ground state. The dynamics of AF-F and F-AF coupling clusters are solved exactly. Each cluster contributes as many long relaxation times as it has non-trivial local energy minima. The barriers against inversion of the clusters take only two values, 0 and 4|J|. In the paramagnetic case (PM), there is no diverging relaxation time. In the ferromagnetic case (FM), there is only one long-lived mode. The longest relaxation times follow an Arrhenius law. Both AF-F and F-AF clusters undergo a zero-temperature phase transition. The real and imaginary parts of the dynamic susceptibility display maxima if plotted versus temperature. The frequency dependence of the susceptibilities explain the effect of frustration. The real part reveals two plateaus and the imaginary part displays two corresponding maxima if they are plotted as functions of the logarithm of frequency. The Argand plots show two overlapping semicircles for fixed frequency at low temperature, indicating the time separation of the modes.

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

“…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.…”

“…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].…”

“…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.…”

Dynamics of Ising spin chains with nearest‐neighbour and next‐nearest‐neighbour interactions in random fields

“…Also, the effects of random fields on the distribution of relaxation times seem to be stronger than those of the exchange fields. All the results obtained here for the relaxation phenomena and their properties are compared with those discussed by Ismail et al for the finite RFI system on a triangular lattice [25,27] and linear chains [15,20]. Generally, we can say that the finite RFI systems in one-and two-dimensional clusters with nn and nnn interactions seem to have similar dynamical behaviours like the SG systems.…”

“…Also, for the RFI model Belanger [7] discusses experiments and Nattermann [7] surveys the theory. They have considered ena, which are important in studying the disordered Ising systems from the magnetic point of view [14,25]. Not only does the model discussed here display a zero-temperature phase transition, but it also has two advantages.…”