期刊
JOURNAL OF STATISTICAL PHYSICS
卷 177, 期 6, 页码 1063-1076出版社
SPRINGER
DOI: 10.1007/s10955-019-02408-y
关键词
Perturbation Hamiltonian; Spontaneous symmetry-breaking; Replica symmetry-breaking; Disordered spin systems; Spin overlap; Self-averaging; The law of large numbers
It is shown that the variance of a perturbation Hamiltonian density vanishes in the infinite-volume limit of perturbed spin systems with quenched disorder. This is proven in a simpler way and under less assumptions than before. A corollary of this theorem indicates the impossibility of non-spontaneous replica symmetry-breaking in disordered spin systems. The commutativity between the infinite-volume limit and the switched-off limit of a replica symmetry-breaking perturbation implies that the variance of the spin overlap vanishes in the replica symmetric Gibbs state.
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