发表机构
Brookhaven National Laboratory（布鲁克海文国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了连接一维统计物理学中集体行为自发与场诱导机制的人机定理，揭示了人机协作可孕育自主科学突破的可能性。
AI 中文摘要
人工智能（AI）能否生成人类合作者主动假设空间（AHS）之外的科学假设？能否组织人机研究以提高此类突破的可能性？我们记录了这样一个案例，同时证明了一个定理，该定理连接了统计物理学的两种基本组织机制：零场下由竞争相互作用产生的集体行为，以及由外场诱导或控制的集体行为。对于所有整数n≥1和所有系统尺寸L≥1，具有任意非均匀最近邻和次近邻相互作用函数U_i(S_i·S_{i+1})与V_i(S_i·S_{i+2})的零场O(n)矢量开链，在哈密顿量层面通过与温度无关的映射，微观等价于更简单的O(n)开链，其最近邻相互作用为V_i(σ_i·σ_{i+1})，轴向单自旋势为U_i(σ_i^z)。齐次线性特例将基础受挫J₁-J₂模型映射到规范J-h场模型——其中n=1、2、3分别对应伊辛（Ising）、XY和海森堡（Heisenberg）经典自旋模型。当连续O(n)自旋替换为具有标准Potts相互作用的q态Potts自旋时，存在类似定理，这意味着对于所有q≥2和所有L≥1，J₁-J₂ Potts开链存在闭式精确解。这些定理源于持续的人机协作，表明在系统研究计划中全程引入AI可能孕育出自主科学突破。
英文摘要
Can an artificial intelligence (AI) generate a scientific hypothesis outside a human collaborator's active hypothesis space (AHS), and can human-AI research be organized to make such breakthroughs more likely? We document such a case while proving a theorem that connects two basic organizing mechanisms of statistical physics: collective behavior arising in zero field from competing interactions and that induced or controlled by an external field. A zero-field $O(n)$-vector open chain with arbitrary inhomogeneous nearest- and next-nearest-neighbor interaction functions $U_i(S_i\cdot{S}_{i+1})$ and $V_i(S_i\cdot{S}_{i+2})$ is microscopically, via a temperature-independent mapping at the Hamiltonian level, equivalent to a simpler $O(n)$ open chain with nearest-neighbor interaction $V_i(\boldsymbolσ_i\cdot\boldsymbolσ_{i+1})$ and axial single-spin potential $U_i(σ_i^z)$ for every integer $n\ge1$ and every system size $L\ge1$. The homogeneous linear specialization maps the foundational frustrated $J_1$-$J_2$ model onto the canonical $J$-$h$ field model---with $n=1,2,3$ being the Ising, XY, and Heisenberg classical spin models, respectively; the theorem resolved a longstanding challenge for $n=3$ published in 1990. Its proof was done with an AI-synthesized recursive Householder moving frame and understood via a human-recognized hidden reciprocity. An analogous theorem holds when the continuous $O(n)$ spins are replaced by the $q$-state Potts spins, implying a closed-form exact solution of the $J_1$-$J_2$ standard Potts open chain for every $q\ge2$ and every $L\ge1$. The emergence of these theorems from a human-AI co-development framework suggests that sustained AI involvement throughout a systematic research program may incubate autonomous scientific breakthroughs and make aspects of the discovery process experimentally testable.
Comments17 pages (extended from 12 pages), 3 figures, 2 tables; added the link and message-level citations to the human-AI conversation transcript [38]
