Moment ratios for an urn model of sand compartmentalization

Numerically solving a master equation for a recently introduced nonequilibrium urn model of sand compartmentalization, we show that the order-parameter moment ratios of the fourth and sixth order remain constant along an exactly located line of critical points. Obtained values are in very good agreement with values predicted by Brézin and Zinn-Justin for the equilibrium Ising model above the critical dimension. At the tricritical point, these ratios acquire values that also agree with a suitably extended Brézin and Zinn-Justin approach.