Volume 118, Number 5, June 2017
|Number of page(s)||7|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||03 August 2017|
Lorentzian symmetry predicts universality beyond scaling laws
School of Mathematics and Statistics, University of Glasgow - University Place, Glasgow G12 8SQ, Scotland, UK
Received: 7 October 2016
Accepted: 16 June 2017
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.
PACS: 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.65.+b – Self-organized systems
© EPLA, 2017
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