Inflow versus outflow zero-temperature dynamics in one dimension

TL;DR

This paper compares inflow (Glauber) and outflow (Sznajd) zero-temperature dynamics in a one-dimensional Ising model, revealing differences through analytical mapping and computational simulations.

Contribution

It introduces a simple mapping to distinguish inflow and outflow dynamics and compares their effects using various updating schemes and metrics.

Findings

Differences are observed between inflow and outflow dynamics.

Mapping reveals inherent distinctions in dynamics.

Relaxation times and persistence vary between the two methods.

Abstract

It has been suggested that Glauber (inflow) and Sznajd (outflow) zero-temperature dynamics for the one dimensional Ising ferromagnet with the nearest neighbors interactions are equivalent. Here we compare both dynamics from analytical and computational points of view. We use the method of mapping an Ising spin system onto the dimer RSA model and show that already this simple mapping allows to see the differences between inflow and outflow zero-temperature dynamics. Then we investigate both dynamics with synchronous, partially synchronous and random sequential updating using the Monte Carlo technique and compare both dynamics in terms of the number of persistent spins, clusters, mean relaxation time and relaxation time distribution.