Droplets in the two-dimensional +-J spin glass: evidence for (non-) universality

Abstract

Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo simulations. Here, using calculations of ground states of suitable perturbed systems, droplets are obtained in two-dimensional +-J spin glasses, which are in the focus of a currently very lifely debate. Since a sophisticated matching algorithm is applied here, exact ground states of large systems up to L^2=256^2 spins can be generated. Furthermore, no equilibration or extrapolation to T=0 is necessary. Three different +-J models are studied here: a) with open boundary conditions, b) with fixed boundary conditions and c) a diluted system where a fraction p=0.125 of all bonds is zero. For large systems, the droplet energy shows for all three models a power-law behavior E_D L^θ'_D with θ'_D<0. This is different from previous studies of domain walls, where a convergence to a constant non-zero value (θ_dw=0) has been found for such models. After correcting for the non-compactness of the droplets, the results are likely to be compatible with θ_D= -0.29 for all three models. This is in accordance with the Gaussian system where θ_D=-0.287(4) (ν=3.5 via ν=-1/θ_D). Nevertheless, the disorder-averaged spin-spin correlation exponent ηis determined here via the probability to have a non-zero-energy droplet, and η~0.22$ is found for all three models, this being in contrast to the behavior of the model with Gaussian interactions, where exactly η=0.