Energy gap of the bimodal two-dimensional Ising spin glass

Abstract

An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a distribution that is neither normal nor lognormal. Nevertheless, it is possible to estimate the most likely value and this is found to scale as L 3 T-2 exp (-4J/kT), for a L × L lattice. Our analysis also explains, for the first time, why a correlation length ξ ∼ exp (2J/kT) is consistent with an energy gap of 2J. Our method allows us to obtain results for up to 105 disorder realizations with L ≤ 96. Distributions of second and third excitations are also shown. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.