论文标题
分层平价模型
The Hierarchical Parity Model
论文作者
论文摘要
层次自旋玻璃是通过递归耦合两个同等大小的子系统来定义的自旋模型。在这项工作中，引入了一个新的分层自旋系统，其中子系统通过旋转的奇偶校验将子系统递归结合在一起。即使是完全通用的耦合，也可以为此层次奇偶校验模型得出许多许多相关因子的精确翻新组递归方程。此外，该模型在计算上是可以进行计算处理的，因为对于分区函数和基态能量的计算，存在$ o（n）$算法。在耦合全部相等的特殊情况下，该模型显示出显示热相变。
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together through the parity of their spins. Exact Renormalization Group recursion equations for many correlators may be derived for this Hierarchical Parity Model, even for completely general couplings. Moreover, the model is computationally tractable in that $O(N)$ algorithms exist for the computation of the partition function and ground state energy. In the special case where the couplings are all equal, the model is shown to exhibit a thermal phase transition.
