二维量子海森堡铁磁体的有限程与长程自旋波自由能渐近行为

中文摘要 AI 辅助

针对具有渐近径向幂律交换的二维量子海森堡铁磁体，我们在每个固定自旋处证明了低温自由能的主导项，该结果在弱场尺度下一致成立。我们得到了与文献[16,17]中色散关系相关的分数及对数修正规律，量子蒙特卡罗模拟为自旋1/2对应的反常磁子色散关系提供了支持。对于具有有限二阶矩的核，我们还推广了最近邻定理[14]，扩展了高桥的二次定律[21]及其弱场依赖关系[11]。

英文摘要

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].

发表机构

• Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）

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