Optimal Size of a Complex Network

TL;DR

This study explores how the size of a small-world network influences the dynamic response of an Ising model under oscillating fields, revealing a resonance-like peak at intermediate temperatures.

Contribution

It identifies the existence of an optimal network size for maximal response in an Ising system on small-world networks, dependent on temperature.

Findings

Occupancy ratio exhibits a resonance-like peak at intermediate temperatures.

At low and high temperatures, response monotonically varies with system size.

Saturation of response occurs at a size depending on temperature.

Abstract

We investigate the response behavior of an Ising system, driven by an oscillating field, on a small-world network, with particular attention to the effects of the system size. The responses of the magnetization to the driving field are probed by means of Monte Carlo dynamic simulations with the rewiring probability varied. It is found that at low and high temperatures the occupancy ratio, measuring how many spins follow the driving field, behaves monotonically with the system size. At intermediate temperatures, on the other hand, the occupancy ratio first grows and then reduces as the size is increased, displaying a resonance-like peak at a finite value of the system size. In all cases, further increase of the size eventually leads to saturation to finite values; the size at which saturation emerges is observed to depend on the temperature, similarly to the correlation length of the system.