Decorated Clusters and Geometrical Frustration in Cluster Spin Glass: A Random Graph Approach

TL;DR

This paper develops a theoretical framework using random graph techniques to study how geometric frustration and impurities in cluster spin glasses influence their phase behavior and magnetic properties.

Contribution

It introduces a model incorporating decorated clusters and impurity effects, analyzing their impact on the Cluster Spin Glass phase using sparse random graph methods.

Findings

Robust geometric frustration persists despite ferromagnetic impurities.

Impurity probability threshold depends on network connectivity.

Impurities influence the paramagnetic phase as seen in Curie-Weiss temperature.

Abstract

We develop a theory to investigate how geometrically frustrated clusters that become decorated affect the Cluster Spin Glass phase. The cluster structure is assumed to be a tetrahedron composed of Ising spins with z-anisotropy placed at its vertices that interact antiferromagnetically. We consider the probability $1-p_J$ of finding an impurity at a vertex of the tetrahedron that interacts ferromagnetically with the remaining elements inside the tetrahedron. An intercluster disorder is added as a random Gaussian interaction. The order parameters are obtained using the sparse random graph technique, which introduces the connectivity of the network of clusters as a controllable parameter in the theory. We examine changes that occur in the Cluster Spin Glass phase as a function of $p_J$ and $c$, in addition to the antiferromagnetic intracluster couplings $J_1$. For intermediate values of $p_J$, unexpected results appear. Even when some clusters contain a ferromagnetic impurity, there will still be robust geometric frustration effects in the cluster network. However, the $p_J$ threshold for this to occur depends on connectivity. Conversely, below this threshold, reduced GF effects favor the reappearance of the CSG phase. Furthermore, the Curie-Weiss temperature $\Theta_W$ has a gradual change of signal, indicating that the effects of the impurities extend to the paramagnetic phase.