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

Abstract

In numerical calculations of a quantity $\ensuremath{\Lambda}(T)\ensuremath{\equiv}\ensuremath{-}\frac{\ensuremath{\partial}\mathrm{ln}{\ensuremath{\chi}}_{\mathrm{EA}}^{{}^{\ensuremath{'}}}}{\ensuremath{\partial}T}$, where ${\ensuremath{\chi}}_{\mathrm{EA}}^{\ensuremath{'}}\ensuremath{\equiv}\ensuremath{\Sigma}{({〈{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{j}〉}_{T}^{2})}_{J}$ for finite $L\ifmmode\times\else\texttimes\fi{}L$ Edwards-Anderson (EA) models, Fern\'andez [Phys. Rev. B 25, 417 (1982)] finds that $\ensuremath{\Lambda}(T)$ has a peak at ${T}_{0}\ensuremath{\approx}0.6$ (Gaussian model) or ${T}_{0}\ensuremath{\approx}1.0$, for $L=4,6,8,10,or 11$, respectively. He finds that the peak height ${\ensuremath{\Lambda}}_{max}=\ensuremath{\Lambda}({T}_{0})$ increases in direct proportion to $L$, and interprets his results in terms of a phase transition at ${T}_{0}$, where the correlation length ${\ensuremath{\xi}}_{\mathrm{EA}}\ensuremath{\propto}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{-}1}$. This conclusion is in disagreement with our previous findings that ${\ensuremath{\xi}}_{\mathrm{EA}}$ is finite in this temperature range, although a (dynamic) "freezing transition" of the spins occurs at ${T}_{f}\ensuremath{\approx}1.0$ (Gaussian model) or ${T}_{f}\ensuremath{\approx}1.3$ ($\ifmmode\pm\else\textpm\fi{}J$ model), which lead us to suggest that the two-dimensional EA model has a phase transition at zero temperature only.