论文标题
高温水龙头上限为平均野外旋转玻璃的自由能
High temperature TAP upper bound for the free energy of mean field spin glasses
论文作者
论文摘要
这项工作证明了Sherrington-Kirkpatrick模型的自由能及其在Thouless-Anderson-Palmer（Tap）Energy方面的概括。结果适用于带球形或伊辛旋转的型号以及任何混合的$ p $ spin hamiltonian与外部场或非线性尖峰术语。预计该结合在高温下会紧密到领先顺序，并且在存在外场的情况下是不平凡的。为了证明，采用了一种几何微域方法，其中一个人用集合覆盖旋转空间，每个方法都以磁化向量$ m $为中心，并且其对分区功能的贡献是根据$ m $ $ m $的TAP能量界定的。
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed $p$-spin Hamiltonian with external field or with a non-linear spike term. The bound is expected to be tight to leading order at high temperature, and is non-trivial in the presence of an external field. For the proof a geometric microcanonical method is employed, in which one covers the spin space with sets, each of which is centered at a magnetization vector $m$ and whose contribution to the partition function is bounded in terms of the TAP energy at $m$.
