Abstract
We study the higher-order cumulant universality of the order-parameter distribution at criticality for the two-dimensional nearest-neighbor ferromagnetic Ising model with Monte Carlo methods. These cumulants are interesting because they are a quantitative measure of the shape of the critical order parameter distribution. This shape has been predicted to be universal. Up to now, only the fourth-order cumulant has been studied in any detail. The set of higher-order cumulants as a whole is more sensitive to the details of the distribution and hence is a stronger test. It cannot be sampled efficiently with standard Monte Carlo sampling. To the best of our knowledge, no definite numerical results have been reported in the literature. Using the umbrella-sampling technique, we are able to obtain accurate estimates for the fourth-, sixth-, eighth-, and tenth-order cumulants for both the square and triangular lattices of different lattice sizes. These results support universality.
Published Version
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