Lorentzian symmetry predicts universality beyond scaling laws

School of Mathematics and Statistics, University of Glasgow - University Place, Glasgow G12 8SQ, Scotland, UK

^(a) Stephen.Watson@glasgow.ac.uk

Received: 7 October 2016
Accepted: 16 June 2017

Abstract

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 domains grows in time t according to , where (the invariant spin-excess) and β is 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.