Defect energy with conjugate boundary conditions in spin-glass models in two dimensions

We calculate the naive defect energy ΔE of Ising spin glass (SG) models in two dimensions using conjugate boundary conditions. We predict that, in the ±J model, the averaged value ΔE converges to some nonzero value in the thermodynamic limit in contrast with ΔE=0 in the Gaussian model. This prediction supports a recent Monte Carlo prediction of the presence of the SG phase at finite temperatures in the ±J Ising model. We also calculate the interface free energy to confirm it.