The Energy-Energy Correlation Function of the Random Bond Ising Model in Two Dimensions

The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising model: one is finite whereas the other is divergent at the critical points. The corresponding exponent of the divergent correlation length is $\nu_e=1/2$ in contrast to the pure system where $\nu_e=1$. The calculation is based on a previously developed effective field theory for the energy density fluctuations.