PreprintCC BY 4.0arXiv
Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet
Abstract
For the two-dimensional quantum Heisenberg ferromagnet with asymptotically radial power-law exchange, we prove the leading low-temperature free energy at every fixed spin, uniformly on the weak-field scale. We obtain fractional and logarithmically corrected laws associated with the dispersions predicted in [16, 17]. Quantum Monte Carlo simulations support the associated anomalous magnon dispersions for spin one-half [20]. For kernels with finite second moment, we also extend the nearest-neighbour theorem [14], generalizing Takahashi's quadratic law [21] and its weak-field dependence [11].
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BibTeX
@misc{klippel2026finite,
title = {{Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet}},
author = {Andreas Klippel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10736},
eprint = {2610.10736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10736},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet
AU - Andreas Klippel
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10736
UR - https://arxiv.org/abs/2610.10736
AB - For the two-dimensional quantum Heisenberg ferromagnet with asymptotically radial power-law exchange, we prove the leading low-temperature free energy at every fixed spin, uniformly on the weak-field scale. We obtain fractional and logarithmically corrected laws associated with the dispersions predicted in [16, 17]. Quantum Monte Carlo simulations support the associated anomalous magnon dispersions for spin one-half [20]. For kernels with finite second moment, we also extend the nearest-neighbour theorem [14], generalizing Takahashi's quadratic law [21] and its weak-field dependence [11].
ER -