自旋系统在淬火无序下的普适采样
Universal sampling of spin systems across quenched disorder
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中文总结 AI 辅助
提出一种基于Transformer的普适神经变分框架，在无序系综中摊销推断，无需逐实例平衡，成功捕捉二维无序自旋系统的临界行为。
中文摘要 AI 辅助
统计物理通过对系统众多微观自由度进行平均来提取宏观规律。无序系统则需要第二次且困难得多的平均，即对淬火随机性本身的平均。经典解析途径，即复制法和空腔法，在平均场或树状极限之外变得不可控，而传统数值算法如并行回火需要对每个无序实现进行昂贵的独立平衡。在本工作中，我们引入了一个普适的神经变分框架，将推断在无序系综上进行摊销，从而消除了对每个实例进行马尔可夫链平衡的需求以及重新训练特定实例变分拟设的成本。该框架基于编码器-解码器Transformer架构，训练一次后，无需进一步优化即可为未见过的无序实现生成玻尔兹曼分布的显式近似。我们在二维Edwards-Anderson模型上验证了该框架，并将其应用于随机键Ising模型，成功捕捉了Nishimori多临界点附近的Binder累积量交叉。这些结果将变分推断的对象从单个实例转移到无序系综，为逐实例计算不可行的阻挫多体系统开辟了道路。
英文摘要
Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.
发表机构
- Beijing University of Posts and Telecommunications（北京邮电大学）
- Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
- Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）
- University of Electronic Science and Technology of China（电子科技大学）
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础科学与数学学院）
- School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）
- School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）
- Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
- School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
机构由 AI 辅助整理，请以论文原文为准。
