Zero temperature dynamics in two dimensional ANNNI model

TL;DR

This paper studies the zero-temperature dynamics of the 2D ANNNI model, revealing different behaviors depending on the parameter , including metastable states, striped states, and unique ground state evolution, with detailed analysis of persistence and domain walls.

Contribution

It provides a comprehensive analysis of the dynamical phases of the 2D ANNNI model at zero temperature, highlighting the effects of the parameter  on the evolution and final states.

Findings

For <1, the system reaches metastable states.

For >1, the system often freezes into striped states.

At =1, the system always reaches the true ground state.

Abstract

We investigate the dynamics of a two dimensional axial next nearest neighbour Ising (ANNNI) model following a quench to zero temperature. The Hamiltonian is given by $H = -J_0\sum_{i,j=1}^L S_{i,j}S_{i+1,j} - J_1\sum_{i,j=1} [S_{i,j} S_{i,j+1} -\kappa S_{i,j} S_{i,j+2}]$. For $\kappa <1$, the system does not reach the equilibrium ground state but slowly evolves to a metastable state. For $\kappa > 1$, the system shows a behaviour similar to the two dimensional ferromagnetic Ising model in the sense that it freezes to a striped state with a finite probability. The persistence probability shows algebraic decay here with an exponent $\theta = 0.235 \pm 0.001$ while the dynamical exponent of growth $z=2.08\pm 0.01$. For $\kappa =1$, the system belongs to a completely different dynamical class; it always evolves to the true ground state with the persistence and dynamical exponent having unique values. Much of the dynamical phenomena can be understood by studying the dynamics and distribution of the number of domains walls. We also compare the dynamical behaviour to that of a Ising model in which both the nearest and next nearest neighbour interactions are ferromagnetic.