On the Possibility of Quasi Small-World Nanomaterials

TL;DR

This paper explores the theoretical possibility of creating nanomaterials with small-world network properties, using Monte Carlo simulations on Ising models to analyze phase transitions and effective critical temperatures.

Contribution

It introduces the concept of quasi small-world nanomaterials and provides simulation-based evidence of their properties and potential synthesis methods.

Findings

Finite-temperature phase transition in one network type.

No phase transition but power-law behavior in another.

Potential synthesis route for quasi small-world nanomaterials.

Abstract

The possibility of materials that are governed by a fixed point related to small world networks is discussed. In particular, large-scale Monte Carlo simulations are performed on Ising ferromagnetic models on two different small-world networks generated from a one-dimensional spin chain. One has the small-world bond strengths independent of the length, and exhibits a finite-temperature phase transition. The other has small-world bonds built from atoms, and although there is no finite-temperature phase transition the system shows a slow power-law change of the effective critical temperature of a finite system as a function of the system size. An outline of a possible synthesis route for quasi small-world nanomaterials is presented.