Quantum phase transitions and conserved charges

The constraints on the scaling properties of conserved charge densities in the vicinity of a zero temperature (T), second-order quantum phase transition are studied. We introduce a generalized Wilson ratio, characterizing the nonlinear response to an external field,H, coupling to any conserved charge, and argue that it is a completely universal function ofH/T: this is illustrated by computations on model systems. We also note implications for transitions where the order parameter is a conserved charge (as in aT=0 ferromagnet-paramagnet transition).