论文标题
在龙头自由能的近似值上
On the REM approximation of TAP free energies
论文作者
论文摘要
平均场自旋玻璃SK模型的Tap-Solutions的自由能可以表示为局部术语的非线性功能：我们利用此功能，以供您构成抽象的REM样模型，然后通过经典的大型偏差处理来解决这些模型。这允许确定对SK模型的Parisi自由能的物理不设置的二次二次校正（在温度往面）的起源，并正式化了$ \ textit {true} $腔动力学，该腔动力学作用于Tap Space，即在Tap-solations的空间上。从非自旋玻璃的角度来看，这项工作是一系列改进中的第一项，该研究涉及不断发展的种群模型中层次结构的稳定性。
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the $\textit{true}$ cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
