Universality of replica symmetry breaking in the transverse field Sherrington-Kirkpatrick model
Universality of replica symmetry breaking in the transverse field Sherrington-Kirkpatrick model
复制标题
横向场谢林顿-柯克帕特里克模型中复制对称破缺的普遍性
DOI：
10.1007/s10955-023-03078-7
复制
发表时间：
2023
影响因子：
1.6
通讯作者：
Sakamoto
中科院分区：
文献类型：
--
作者：
Itoi;Ishimori;Sato;Sakamoto
将横向场 Sherrington-Kirkpatrick (SK) 模型中复制对称破缺 (RSB) 的存在定理推广到具有一般随机交换相互作用的模型。对于一般随机相互作用，交换相互作用能的期望值与自旋算子的杜哈梅尔相关函数之间的关系可以通过分部近似积分得到。除了 Falk-Bruch 不等式之外，这些显式评估使我们能够证明，在足够低的温度下，在足够弱的横向场下，两个副本自旋算子之间的重叠方差不会消失。铁磁长程有序的缺失也被证明可以将 RSB 与对称性破缺区分开来。
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-symmetry breaking.