Self-averaging of perturbation Hamiltonian density in perturbed spin systems
arXiv:1908.09423 · doi:10.1007/s10955-019-02408-y
Abstract
It is shown that the variance of a perturbation Hamiltonian density vanishes in the infinite-volume limit of the 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.
13 pages. arXiv admin note: text overlap with arXiv:1811.04386