Zero-temperature Glauber dynamics on small-world networks

TL;DR

This study investigates how zero-temperature Glauber dynamics behaves on small-world networks derived from a 2D lattice, revealing that increased disorder accelerates reaching ground states in finite networks but not in the thermodynamic limit.

Contribution

It provides new insights into the dynamics of the Ising model on small-world networks, especially how disorder affects the speed of reaching equilibrium and the decay of spin correlations.

Findings

Faster dynamics with increased disorder in finite networks.

Probability of reaching ground state vanishes in the thermodynamic limit for any finite rewiring probability.

Correlation length scales with rewiring probability as lambda ~ p^(-0.73).

Abstract

The zero-temperature Glauber dynamics of the ferromagnetic Ising model on small-world networks, rewired from a two-dimensional square lattice, has been studied by numerical simulations. For increasing disorder in finite networks, the nonequilibrium dynamics becomes faster, so that the ground state is found more likely. For any finite value of the rewiring probability p, the likelihood of reaching the ground state goes to zero in the thermodynamic limit, similarly to random networks. The spin correlation xi(r) is found to decrease with distance as xi(r) ~ exp(-r/lambda), lambda being a correlation length scaling with p as lambda ~ p^(-0.73). These results are compared with those obtained earlier for addition-type small world networks.