Domain wall entropy of the bimodal two-dimensional Ising spin glass

Abstract

We report calculations of the domain wall entropy for the bimodal two-dimensional Ising spin glass in the critical ground state. The $L\ifmmode\times\else\texttimes\fi{}L$ system sizes are large with $L$ up to $256$. We find that it is possible to fit the variance of the domain wall entropy to a power function of $L$. The data were obtained using an algorithm that works exactly in the ground state. The integrity of the floating point arithmetic was rigorously checked against exact results for correlation functions and some disorder realizations were run in arbitrary precision as necessary. Nevertheless, in spite of the excellent integrity of the results, the quality of the data distributions are unsatisfactory with large $L>96$. Consequently, it is not possible to reliably determine the fractal dimension of the domain walls.