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

Abstract

We calculate the naive defect energy $\ensuremath{\Delta}E$ of Ising spin glass (SG) models in two dimensions using conjugate boundary conditions. We predict that, in the $\ifmmode\pm\else\textpm\fi{}J$ model, the averaged value $\ensuremath{\Delta}E\ifmmode\bar\else\textasciimacron\fi{}$ converges to some nonzero value in the thermodynamic limit in contrast with $\ensuremath{\Delta}E\ifmmode\bar\else\textasciimacron\fi{}=0$ in the Gaussian model. This prediction supports a recent Monte Carlo prediction of the presence of the SG phase at finite temperatures in the $\ifmmode\pm\else\textpm\fi{}J$ Ising model. We also calculate the interface free energy to confirm it.