Dynamics of Ising spins with antiferromagnetic bonds on a triangular lattice

Six-coupled Ising spins on a triangular lattice with antiferromagnetic (AF) nearest neighbour and ferro-magnetic (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 DeltaE = 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\textbackslash{}J\textbackslash{}. 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.