论文标题
通过通用混合$ P $ -SPIN模型中的空腔方法在Tap方程式上
On the TAP equations via the cavity approach in the generic mixed $p$-spin models
论文作者
论文摘要
1977年，Thou Leless，Anderson和Palmer（Tap）根据有效磁化的方程式得出了一个一致方程式系统，以便研究Sherrington-Kirkpatrick（SK）Spin玻璃模型中的自由能。预计其方程式的解决方案包含有关SK Hamiltonian和Tap Free Energy的景观的重要信息，此外，与Parisi的复制品Ansatz有直接的联系。在这项工作中，我们旨在调查TAP方程在通用混合$ P $ -SPIN模型中的有效性。通过利用重叠的超质量，我们表明，通过在渐近纯状态下的有条件局部磁化，TAP方程是渐近满足的。
In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi's replica ansatz. In this work, we aim to investigate the validity of the TAP equations in the generic mixed $p$-spin model. By utilizing the ultrametricity of the overlaps, we show that the TAP equations are asymptotically satisfied by the conditional local magnetizations on the asymptotic pure states.
