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Self-Averaging of Perturbation Hamiltonian Density in Perturbed Spin Systems

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Abstract

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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Authors and Affiliations

  1. Department of Physics, GS & CST, Nihon University, Tokyo, Japan

    C. Itoi

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  1. C. Itoi
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Correspondence to C. Itoi.

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Communicated by Hal Tasaki.

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Itoi, C. Self-Averaging of Perturbation Hamiltonian Density in Perturbed Spin Systems. J Stat Phys 177, 1063–1076 (2019). https://doi.org/10.1007/s10955-019-02408-y

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