Binder cumulants of an urn model and Ising model above critical dimension

Abstract

Solving numerically master equation for a recently introduced urn model, we show that the fourth- and sixth-order cumulants remain constant along an exactly located line of critical points. Obtained values are in very good agreement with values predicted by Brezin and Zinn-Justin for the Ising model above the critical dimension. At the tricritical point cumulants acquire values which also agree with a suitably extended Brezin and Zinn-Justin approach.