Magnetic Small World Nanomaterials: Physical Small World Networks

TL;DR

This paper explores the feasibility and properties of magnetic small world networks constrained by physical factors, analyzing their spectral characteristics and phase transition behavior in Ising models.

Contribution

It introduces the concept of physical small world networks with realistic constraints and studies their impact on critical phenomena in magnetic models.

Findings

Physical small world networks can exist under certain conditions.

Small world connections influence the critical behavior of Ising models.

Spectral analysis reveals unique properties of these networks.

Abstract

The question addressed is whether magnetic materials based on physical small world networks are possible. Physical constraints, such as uniform bond length and embedding in three dimensions, are the new features added to make small world networks physical. Results are presented to further determine if physical small world networks can exist, and the effect of the small world connections on the critical phenomena of Ising models on such networks. Spectra of the Laplacian on randomly-collapsed bead-chain networks are studied. The scaling function for the order parameter of an Ising model with physical small world connections is presented.