Ising model simulation in directed lattices and networks

TL;DR

This paper investigates the behavior of the Ising model on directed lattices and networks, revealing the absence of spontaneous magnetisation and characterizing decay times, with implications for understanding magnetic phenomena in directed structures.

Contribution

It provides new insights into the Ising model's behavior on directed lattices and networks, including decay laws and the effects of different algorithms.

Findings

No spontaneous magnetisation on directed lattices in lower dimensions.

Decay time follows an Arrhenius law on square and cubic lattices.

Different algorithms show similar or exponential decay behaviors on networks.

Abstract

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.