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Decorated clusters and geometrical frustration in cluster spin glass: A random graph approach

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  • Magalhães, S.G.
  • Zimmer, F.M.
  • Erichsen, R.

Abstract

We investigate the effects of geometric frustration on the cluster spin glass phase using tetrahedral clusters of Ising spins with disordered intercluster interactions. The sparse random graph technique is employed to treat these intercluster interactions, introducing a cluster network with connectivity controlled by a parameter. Inside the tetrahedral clusters, the interactions are antiferromagnetic, but there is a finite probability that a vertex is occupied by an impurity (decorated) that couples ferromagnetically to the remaining spins. Our findings suggest that at low impurity concentrations, geometric frustration remains robust in the cluster network, suppressing the cluster spin glass phase. However, above this threshold, the situation is completely reversed: the effects of geometric frustration are weakened, favoring the emergence of the cluster spin glass phase. Furthermore, the Curie–Weiss temperature exhibits a gradual change in sign, indicating that the influence of the ferromagnetic impurities extends into the paramagnetic phase.

Suggested Citation

  • Magalhães, S.G. & Zimmer, F.M. & Erichsen, R., 2026. "Decorated clusters and geometrical frustration in cluster spin glass: A random graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
    • Handle: RePEc:eee:phsmap:v:681:y:2026:i:c:s0378437125007897
    DOI: 10.1016/j.physa.2025.131137
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    References listed on IDEAS

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    1. Schmidt, M. & Zimmer, F.M. & Magalhaes, S.G., 2015. "Spin glass induced by infinitesimal disorder in geometrically frustrated kagome lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 416-423.
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