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

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 $\gamma_{eff}$ 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.Comment: 6 pages, 4 figure

Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet

It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrated that the data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer

Ising model on 3D random lattices: A Monte Carlo study

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and \phi^4 field theory on three-dimensional regular cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure