Spin-wave theory on hyperbolic lattices shows Goldstone modes have vanishing local weight and a bulk gap, allowing finite-temperature magnetic order that evades the Mermin-Wagner theorem.
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Generalizes LSM theorem to hyperbolic lattices with Fuchsian symmetry and derives lower bound on ground-state degeneracy versus filling and geometry.
Fractal lattices like the Sierpiński carpet suppress d-wave superconductivity at half filling while strongly enhancing extended s-wave pairing at other fillings through geometric frustration of sign-changing order parameters.
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Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices
Spin-wave theory on hyperbolic lattices shows Goldstone modes have vanishing local weight and a bulk gap, allowing finite-temperature magnetic order that evades the Mermin-Wagner theorem.
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Lieb-Schultz-Mattis constraints for hyperbolic lattices
Generalizes LSM theorem to hyperbolic lattices with Fuchsian symmetry and derives lower bound on ground-state degeneracy versus filling and geometry.
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Extended Hubbard model on fractals: d-Wave superconductivity and competing pairing channels
Fractal lattices like the Sierpiński carpet suppress d-wave superconductivity at half filling while strongly enhancing extended s-wave pairing at other fillings through geometric frustration of sign-changing order parameters.