具有 $1/r^4$ 相互作用的二维 $XY$ 模型中的对数准长程有序和新颖连续相变

中文摘要 AI 辅助

我们研究了相互作用按 $1/r^{2+\sigma}$ 衰减的二维经典 $XY$ 模型的相图和临界性质。在边缘情况 $\sigma=2$ 下，我们表明低温相的特征是对数准长程有序（log-QLRO），其中自旋关联按距离对数的幂次衰减，$C(r)\sim(\ln r)^{-\eta_\ell}$，且 $\eta_\ell\propto T$，并且进入该相的转变是超越 Ginzburg-Landau-Wilson 范式和 Berezinskii-Kosterlitz-Thouless 机制的连续相变。我们的分析结合了近精确的高斯自旋波理论、绝热重正化群分析和大规模蒙特卡罗模拟。我们发现 $1/r^4$ 相互作用以 $\gamma(k)\simeq\kappa k^2\ln(1/k)$ 的形式对数修正自旋波刚度核，这抑制了涡旋增殖并产生了非普适的关联长度指数 $\nu\propto1/\sqrt{2\pi\kappa}$。至关重要的是，我们的模拟揭示，对于 $\sigma\le2$，短程代数 QLRO 相在弱长程扰动下不稳定。这些结果确立了 $\sigma=2$ 作为长程和短程普适类之间的交叉边界，并为近期的理论提议提供了关键评估。

英文摘要

We investigate the phase diagram and critical properties of the two-dimensional classical XY model with interactions decaying as $1/r^{2+σ}$. At the marginal case $σ=2$, we show that the low-temperature phase is characterized by logarithmic quasi-long-range order (log-QLRO), where spin correlations decay as a power of the logarithm of distance, $C(r)\sim(\ln r)^{-η_\ell}$ with $η_\ell\propto T$, and that the transition into this phase is a continuous transition beyond both the Ginzburg-Landau-Wilson paradigm and the Berezinskii-Kosterlitz-Thouless mechanism. Our analysis combines a near-exact Gaussian spin-wave theory, an adiabatic renormalization-group analysis, and large-scale Monte Carlo simulations. We find that the $1/r^4$ interaction logarithmically modifies the spin-wave stiffness kernel as $γ(k)\simeqκk^2\ln(1/k)$, which suppresses vortex proliferation and gives rise to a nonuniversal correlation-length exponent $ν\propto1/\sqrt{2πκ}$. Crucially, our simulations reveal that the short-range algebraic QLRO phase is unstable against a weak long-range perturbation for $σ\le2$. These results establish $σ=2$ as the crossover boundary between the long-range and short-range universality classes and provide a critical evaluation of recent theoretical proposals.

发表机构

• Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院、微观尺度物理国家研究中心）
• Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
• Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究中心与中科院量子信息科学与技术重点实验室）
• College of Physics, Guizhou University（贵州大学物理学院）

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