AI 中文总结
本文确定了混合偶 $p$-自旋模型在固定外场下的极限重叠结构，证明其收敛到 Parisi 测度，并建立了 Ghirlanda-Guerra 恒等式及零场模型的温度混沌现象。
AI 中文摘要
我们确定了混合偶 $p$-自旋模型（包括 Sherrington-Kirkpatrick 模型）在任意固定确定性外场下的极限重叠结构。特别地，我们证明了无序平均的重叠分布（在零场下为其绝对值）收敛到 Parisi 测度。我们利用相关的 Ruelle 概率级联的重叠数组来识别完整的极限数组。我们还建立了相应的 Ghirlanda-Guerra 恒等式，并确定了淬火重叠分布的极限律。对于零场 Sherrington-Kirkpatrick 模型，我们还证明了在每一对不同非负逆温度下存在温度混沌现象。
英文摘要
We identify the limiting overlap structure of mixed even $p$-spin models, including the Sherrington-Kirkpatrick model, at every fixed deterministic external field. In particular, we show that the disorder-averaged distribution of the overlap, or its absolute value at zero field, converges to the Parisi measure. We identify the full limiting array using the overlap array of the associated Ruelle probability cascade. We also establish the corresponding Ghirlanda-Guerra identities and determine the limiting law of the quenched overlap distribution. For the zero-field Sherrington-Kirkpatrick model, we additionally prove temperature chaos at every pair of distinct nonnegative inverse temperatures.
