Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices

• URL: http://arxiv.org/abs/2606.27422v1
• Date: Thu, 25 Jun 2026 18:00:01 GMT
• Title: Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices
• Abstract summary: Infrared singularities of gapless Goldstone modes preclude magnetic long-range order at finite temperature in conventional two-dimensional systems.<n>We find that the zero-energy collective modes required by symmetry carry vanishing local spectral weight.<n>We estimate the ordering temperature from the thermal spin-wave correction to the ordered moment.
• Score: 45.88028371034407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Infrared singularities of gapless Goldstone modes preclude magnetic long-range order at finite temperature in conventional two-dimensional systems. By studying the spin-$S$ Heisenberg model on regular tilings of the hyperbolic plane, we show that this obstruction is absent in negatively curved space. Using spin-wave theory, we find that the zero-energy collective modes required by symmetry carry vanishing local spectral weight and are separated from the thermodynamic bulk magnon continuum by a finite gap in the bulk local spectral density. As a result, local transverse correlations remain short ranged, with a finite correlation length, despite the presence of Goldstone modes associated with the broken SO(3) spin-rotation symmetry. Stronger negative curvature is found to suppress quantum fluctuations in bulk thermodynamic quantities, pushing the ordered state toward "mean-field-like" behavior. We further estimate the ordering temperature from the thermal spin-wave correction to the ordered moment. These results establish hyperbolic geometry as a route to finite-temperature magnetic order that circumvents the Mermin-Wagner obstruction without breaking or modifying the continuous symmetry.

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