Persistence and dynamics in ANNNI chain

TL;DR

This paper studies the persistence behavior in the ANNNI model, revealing different decay patterns depending on interaction ratios and highlighting its distinct dynamics from the nearest neighbor Ising model.

Contribution

It provides a detailed analysis of local and global persistence in the ANNNI model, identifying how decay patterns change with interaction parameters and comparing its dynamics to the Ising model.

Findings

For $<1$, $P(t)$ decays as a stretched exponential.

For $>1$, $P(t)$ exhibits algebraic decay with a different exponent.

The ANNNI model shows distinct dynamical behavior from the nearest neighbor Ising model.

Abstract

We investigate both the local and global persistence behaviour in ANNNI (axial next-nearest neighour Ising) model. We find that when the ratio $\kappa $ of the second neighbour interaction to the first neighbour interaction is less than 1, $P(t)$, the probability of a spin to remain in its original state upto time $t$ shows a stretched exponential decay. For $\kappa > 1$, $P(t)$ has a algebraic decay but the exponent is different from that of the nearest neighbour Ising model. The global persistence behaviour shows similar features. We also conduct some deeper investigations in the dynamics of the ANNNI model and conclude that it has a different dynamical behaviour compared to the nearest neighbour Ising model.