The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model

Abstract

We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude and the sample dependent pseudo-critical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration $q$ of the empty sites for all investigated values of $q\le 0.25$. At the same time the average effective exponent $γ_{eff}$ is found to vary with the concentration $q$, which may be argued to be due to logarithmic corrections to the power law of the pure system. This corrections are canceled in the susceptibility amplitude ratio as predicted by theory. The central charge of the corresponding field theory was computed and compared well with the theoretical predictions.