Abstract:
Let {E Σ (N)} ΣΣN be a family of |Σ N |=2N centered unit Gaussian random variables defined by the covariance matrix C N of elements c N (Σ,τ):=Av(E Σ (N)E τ (N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N 1 +N 2 , and all pairs (Σ,τ)Σ N ×Σ N :
where π k (Σ),k=1,2 are the projections of ΣΣ N into Σ Nk . The condition is explicitly verified for the Sherrington-Kirkpatrick, the even p-spin, the Derrida REM and the Derrida-Gardner GREM models.
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Received: 17 June 2002 / Accepted: 31 October 2002 Published online: 21 February 2003
Communicated by M. Aizenman
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Contucci, P., Esposti, M., Giardinà, C. et al. Thermodynamical Limit for Correlated Gaussian Random Energy Models. Commun. Math. Phys. 236, 55–63 (2003). https://doi.org/10.1007/s00220-003-0803-y
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DOI: https://doi.org/10.1007/s00220-003-0803-y