Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

TL;DR

This paper investigates the presence of spin glass phases in the antiferromagnetic Heisenberg model on scale-free networks, revealing that such phases occur without traditional randomness from ferromagnetic and antiferromagnetic couplings.

Contribution

It demonstrates the existence of spin glass behavior in the Heisenberg model on scale-free networks, expanding understanding of spin glasses beyond regular lattices.

Findings

Spin glass phase observed for all studied connectivity densities.

Critical temperatures for spin glass transition estimated.

Spin glass behavior occurs without mixed ferromagnetic and antiferromagnetic couplings.

Abstract

Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi {\it et al.} [Phys. Rev. B{\bf 73}, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in $d$-dimensional regular lattices for ($d \leq 3$). We can make an analogy for the connectivity density ($m$) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of $m$ for the existence of SG behaviour, analogous to the lower critical dimension ($d_l$) for the canonical SG systems. Here we study system with $m=2,3,4$ and $5$. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of $m$ and estimated its corersponding critical temperature.