论文标题
横向场中的复制对称性破坏的通用性Sherrington-Kirkpatrick模型
Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model
论文作者
论文摘要
横向场Sherrington-Kirkpatrick（SK）模型中复制对称性破坏（RSB）的存在定理扩展到具有一般随机交换相互作用的模型。交换相互作用能的期望值与自旋算子的Duhamel相关函数之间的关系可以通过零件的近似集成来获得一般随机相互作用。除了Falk-bruch不平等外，这些明确的评估还使我们能够证明，在足够低的温度下，两个复制品自旋算子之间重叠的差异不会消失。还显示缺乏铁磁远距离顺序，可以将RSB与$ \ Mathbb Z_2 $ - 对称性断裂区分开。
The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the exchange interaction energy and the Duhamel correlation function of spin operators can be obtained by an approximate integration by parts for general random interactions. In addition to the Falk-Bruch inequality, these explicit evaluations enable us to prove that the variance of overlap between two replica spin operators does not vanish under sufficiently weak transverse field in sufficiently low temperature. The absence of the ferromagnetic long range order is also shown to distinguish RSB from the $\mathbb Z_2$-symmetry breaking.
