Magnetism of frustrated regular networks

TL;DR

This study investigates how increasing clustering in a regular random network affects antiferromagnetic Ising spins, revealing a transition from antiferromagnetic order to spin-glass behavior as clustering grows.

Contribution

It provides a detailed analysis of the impact of clustering on magnetic phase transitions in regular networks using Monte Carlo simulations and compares results with Bethe approximation predictions.

Findings

Critical temperature decreases with increasing clustering coefficient.

Transition from antiferromagnetic to spin-glass phase observed.

Monte Carlo results align with theoretical predictions for spin-glass behavior.

Abstract

We consider a regular random network where each node has exactly three neighbours. Ising spins at the network nodes interact antiferromagnetically along the links. The clustering coefficient $C$ is tuned from zero to 1/3 by adding new links. At the same time, the density of geometrically frustrated links increases. We calculate the magnetic specific heat, the spin susceptibility and the Edwards-Anderson order parameter $q$ by means of the heat-bath Monte Carlo simulations. The aim is the transition temperature $T_x$ dependence on the clustering coefficient $C$. The results are compared with the predictions of the Bethe approximation. At C=0, the network is bipartite and the low temperature phase is antiferromagnetic. When $C$ increases, the critical temperature falls down towards the values which are close to the theoretical predictions for the spin-glass phase.