We study the ground-state properties of a family of frustrated spin-1/2 Heisenberg models on two-and three-dimensional decorated lattices composed of connected star-shaped units. Each star is built from edge-sharing triangles with an antiferromagnetic interaction on the shared side and ferromagnetic interactions on the others.At a critical coupling ratio, the ideal star model -defined by equal ferromagnetic interactions -exhibits a macroscopically degenerate ground state, which we map onto a site percolation problem on the Lieb lattice. This mapping enables the calculation of exponential ground-state degeneracy and the corresponding residual entropy for square, triangular, honeycomb, and cubic lattices. Remarkably, the residual entropy remains high for all studied lattices, exceeding 60% of the maximal value ln(2). Despite a gapless quadratic one-magnon spectrum, the low-temperature thermodynamics is governed by exponentially numerous gapped excitations. For a distorted-star variant of the model, the ground-state manifold is equivalent to that of decoupled ferromagnetic clusters, leading to exponential degeneracy with a lower, yet still substantial, residual entropy. At low temperature the system mimics a paramagnetic crystal of non-interacting spins with high spin value (s = 4 for a square lattice).The obtained results establish a structural design principle for engineering quantum magnets with a high ground-state degeneracy, suggesting promising candidates for enhanced magnetocaloric cooling and quantum thermal machines.
Dmitriev et al. (Tue,) studied this question.