AI 中文总结
研究三维量子海森堡反铁磁体中体和表面临界性的对数修正，结合量子蒙特卡罗模拟与边界重整化群分析，验证体有限尺寸标度，推导边界关联修正指数及标度形式，发现异常区域的长程表面磁序等。
AI 中文摘要
在体上临界维度，边缘无关相互作用对平均场标度产生乘性对数修正。虽然这些修正对体可观测量已被充分理解，但它们对边界临界性的影响，特别是对有限尺寸标度的影响，仍较少被探索。本文结合大规模量子蒙特卡罗模拟和边界重整化群分析来研究(3 + 1)D O(3)量子临界点。在验证了已知的对数修正体有限尺寸标度后，我们调整表面耦合以识别普通、特殊和异常边界区域。对于普通和特殊转变，我们推导了边界关联的对数修正指数和依赖于\(\hat{\coppa}\)的有限尺寸标度形式，这些预测得到了蒙特卡罗数据的定量支持。在异常区域，我们发现了长程表面磁序和对数增强的表面 - 体关联。
英文摘要
At the bulk upper critical dimension, marginally irrelevant interactions generate multiplicative logarithmic corrections to mean-field scaling. While these corrections are well understood for bulk observables, their consequences for boundary criticality, particularly for finite-size scaling, remain much less explored. Here we combine large-scale quantum Monte Carlo simulations with boundary renormalization-group analysis to study a (3 + 1)D O(3) quantum critical point. After verifying the known logarithmically modified bulk finite-size scaling, including the correlation-length scaling governed by the logarithmic finite-size exponent \hat{\coppa}, we tune the surface coupling to identify ordinary, special, and extraordinary boundary regimes. For the ordinary and special transitions, we derive logarithmic correction exponents and \hat{\coppa}-dependent finite-size scaling forms for boundary correlations, including results that have not been systematically established before. These predictions are quantitatively supported by Monte Carlo data. In the extraordinary regime, we find long-range surface magnetic order and a logarithmically enhanced surface-bulk correlation.
