Lorentzian symmetry predicts universality beyond scaling laws
We present a covariant theory for the ageing characteristics of phase-ordering systems that possess dynamical symmetries beyond mere scalings. A chiral spin dynamics which conserves the spin-up (+) and spin-down (−) fractions, 
and 
, serves as the emblematic paradigm of our theory. Beyond a parabolic spatio-temporal scaling, we discover a hidden Lorentzian dynamical symmetry therein, and thereby prove that the characteristic length L of spin domainsgrows in time t according to 
, where 
(the invariant spin-excess) and βis a universal constant. Furthermore, the normalised length distributions of the spin-up and the spin-down domains each provably adopt a coincident universal (σ-independent) time-invariant form, and this supra-universal probability distribution is empirically verified to assume a form reminiscent of the Wigner surmise.