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Main Authors: Magalhaes, S. G., Zimmer, F. M., Erichsen Jr, R.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.22690
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author Magalhaes, S. G.
Zimmer, F. M.
Erichsen Jr, R.
author_facet Magalhaes, S. G.
Zimmer, F. M.
Erichsen Jr, R.
contents 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 $Θ_W$ has a gradual change of signal, indicating that the effects of the impurities extend to the paramagnetic phase.
format Preprint
id arxiv_https___arxiv_org_abs_2507_22690
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Decorated Clusters and Geometrical Frustration in Cluster Spin Glass: A Random Graph Approach
Magalhaes, S. G.
Zimmer, F. M.
Erichsen Jr, R.
Statistical Mechanics
Disordered Systems and Neural Networks
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 $Θ_W$ has a gradual change of signal, indicating that the effects of the impurities extend to the paramagnetic phase.
title Decorated Clusters and Geometrical Frustration in Cluster Spin Glass: A Random Graph Approach
topic Statistical Mechanics
Disordered Systems and Neural Networks
url https://arxiv.org/abs/2507.22690