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A quantum spin system with random interactions I

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Abstract

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τt(ω)}ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τt(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries which implement τ(ω) in the GNS representation is also almost surely independent of ω.

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Authors and Affiliations

  1. Indian Statistical Institute, Stat. Math. Unit, 560 059, Bangalore, India

    Stephen Dias Barreto

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  1. Stephen Dias Barreto
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Correspondence to Stephen Dias Barreto.

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Barreto, S.D. A quantum spin system with random interactions I. Proc. Indian Acad. Sci. (Math. Sci.) 110, 347–356 (2000). https://doi.org/10.1007/BF02829530

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  • DOI: https://doi.org/10.1007/BF02829530

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