Exact critical behavior of a random bond two-dimensional Ising model

A 2D Ising model in which the bonds K fluctuate randomly about Kc, the critical value of the pure system, is considered. The ensemble average of the square of the two-point function, s₀{s}R〉²{〉}Av$, is shown to decay as (lnR${)}1/4R^-1/2 aat the critical point. This implies that s₀{s}RAv is bounded above by (lnR)1/8{R}^{{{-}}1/4}$ in disagreement with the exp [-(ln lnR${)}²$] decay law found by Dotsenko and Dotsenko by a different method. On the other hand, the present calculation reproduces their specific-heat singularity C{~}ln{}ln{τ}{} ({τ}=K-Kc).