发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用蒙特卡洛数据和机器学习，训练可微求解器预测三维伊辛模型的涌现体几何，发现单一经典度量无法同时拟合两个边界算子的两点函数，量化了算子间的张力并证明其稳健性。
AI 中文摘要
我们利用临界温度下三维伊辛模型的蒙特卡洛数据，通过机器学习预测体（bulk）的涌现径向几何。具体而言，我们采用一个在渐近$\mathrm{AdS}_4$背景上的探针场的可微求解器，训练其复现边界算子（$\sigma$和$\epsilon$）的实测动量空间两点函数。我们发现，单一度量无法同时服务于这两个算子。分别拟合每个通道可将自身残差提高三到五倍，但会使另一通道的残差恶化最多达两个数量级。我们量化了这两个算子之间的这种张力，并表明它不受动量窗口和晶格尺寸变化的影响。我们的结果数值上证明，具有$\mathcal{O}(1)$中心荷的理论（如三维伊辛模型）的体几何不能被单一经典度量所捕获。
英文摘要
We use Monte Carlo data for the three-dimensional Ising model at the critical temperature to predict an emergent radial geometry of the bulk using machine learning. Specifically, we employ a differentiable solver for a probe field on an asymptotically $\mathrm{AdS}_4$ background, trained to reproduce the measured momentum-space two-point functions of the boundary operators ($σ$ and $ε$). We find that a single metric cannot simultaneously serve both operators. Fitting each channel separately improves its own residual by a factor of three to five, but degrades the other by up to two orders of magnitude. We quantify this tension between the two operators and show that it survives changes to the momentum window and the lattice size. Our results numerically demonstrate that the bulk geometry of a theory with an $\mathcal{O}(1)$ central charge, such as the 3D Ising model, is not captured by a single classical metric.
