Periodic planar lattices are built via iterative triangulation to have arbitrarily high Ising critical temperatures, with Tc scaling as (2/ln2) ln q_max and Apollonian lattices conjectured optimal.
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Hybrid Kitaev-Yao-Lee models on common lattices produce magnetic order in spins while preserving orbital topological order, and regain exact solvability when Yao-Lee and square-lattice couplings are equal and opposite.
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Families of planar lattices with arbitrarily high $T_{\rm c}$ for the ferromagnetic Ising model
Periodic planar lattices are built via iterative triangulation to have arbitrarily high Ising critical temperatures, with Tc scaling as (2/ln2) ln q_max and Apollonian lattices conjectured optimal.
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Frustrated magnetic order in hybrid Kitaev spin-orbital models
Hybrid Kitaev-Yao-Lee models on common lattices produce magnetic order in spins while preserving orbital topological order, and regain exact solvability when Yao-Lee and square-lattice couplings are equal and opposite.