Double universality of a quantum phase transition in spinor condensates: the Kibble-\.Zurek mechanism and a conservation law

We consider a phase transition from antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We demonstrate the occurrence of two scaling laws, for the number of spin fluctuations just after the phase transition, and for the number of spin domains in the final, stable configuration. Only the first scaling can be explained by the standard Kibble-\.Zurek mechanism. We explain the occurrence of two scaling laws by a model including post-selection of spin domains due to the conservation of condensate magnetization.