Comment on "Canonical-ensemble results for the Ising model with random bonds in two dimensions"

Abstract

In numerical calculations of a quantity Λ(T)≡-∂lnχEA′/∂T, where χEA′≡Σ(〈σiσj〉T2)J for finite L×L Edwards-Anderson (EA) models, Fernández [Phys. Rev. B 25, 417 (1982)] finds that Λ(T) has a peak at T0≈0.6 (Gaussian model) or T0≈1.0, for L=4,6,8,10,or 11, respectively. He finds that the peak height Λmax=Λ(T0) increases in direct proportion to L, and interprets his results in terms of a phase transition at T0, where the correlation length ξEA∝(T-T0)-1. This conclusion is in disagreement with our previous findings that ξEA is finite in this temperature range, although a (dynamic) "freezing transition" of the spins occurs at Tf≈1.0 (Gaussian model) or Tf≈1.3 (±J model), which lead us to suggest that the two-dimensional EA model has a phase transition at zero temperature only

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