Zero temperature ordering dynamics in two dimensional BNNNI model

Abstract

We investigate the dynamics of a two dimensional bi-axial next nearest neighbour Ising (BNNNI) model following a quench to zero temperature. The Hamiltonian is given by $H=-J_0{\sum }_{i,j=1}^L[(S_{i,j}{S}_{i+1,j}+S_{i,j}{S}_{i,j+1})-\kappa (S_{i,j}{S}_{i+2,j}+S_{i,j}{S}_{i,j+2})]$ . For $\kappa <1$, the system does not reach the equilibrium ground state and keep evolving in active states for ever. For $\kappa \ge 1$, though the system reaches a final state, but it do not reach the ground state always and freezes to a striped state with a finite probability like two dimensional ferromagnetic Ising model and ANNNI model. The overall dynamical behaviour for $\kappa >1$ and $\kappa =1$ is quite different. The residual energy decays in a power law for both $\kappa >1$ and $\kappa =1$ from which the dynamical exponent $z$ have been estimated. The persistence probability shows algebraic decay for $\kappa >1$ with an exponent $\theta =0.22\pm 0.002$ while the dynamical exponent for ordering $z=2.33\pm 0.01$. For $\kappa =1$, the system belongs to a completely different dynamical class with $\theta =0.332\pm 0.002$ and $z=2.47\pm 0.04$. We have computed the freezing probability for different values of $\kappa$. We have also studied the decay of autocorrelation function with time for different regime of $\kappa$ values. The results have been compared with that of the two dimensional ANNNI model.

11 pages, 19 figures

References in corpus (4)

• A new model of binary opinion dynamics: coarsening and effect of disorder
• Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Zero temperature dynamics in two dimensional ANNNI model

Cited by in corpus (1)

• Ballistic annihilation in one dimension : A critical review