Dynamical Multiscaling in Quenched Skyrme Systems

– Strong dynamical scaling violations exist in quenched two-dimensional systems with vector O(3) order parameters. These systems support non-singular topologically stable configurations (skyrmions). By tuning the stability of isolated skyrmions to expand or shrink, we find dramatic differences in the dynamical multiscaling spectrum of decaying moments 〈|ρ|〉 of the topological charge density distribution and in particular in the decay of the energy-density ǫ ∼ 〈|ρ|〉. We present a simple two-length-scale model for the observed exponents in the case when isolated skyrmions expand. No such simple model is found when isolated skyrmions shrink. Phase-ordering systems quenched from disordered initial conditions into an ordered phase typically evolve correlations that dynamically scale — they are self-similar in time [1]. Dynamical scaling provides a powerful framework for the analysis of phase-ordering exponents and correlations. To understand scaling, systems that violate scaling are important to study. Logarithmic scaling violations exist in the spherical limit of conserved vector systems [2]. Recently, strong scaling violations have been found in one-dimensional [3] and two-dimensional (2D) [4, 5] systems supporting non-singular topological textures (“skyrmions”). In this paper we investigate the phase-ordering process of the 2D O(3) vector model in more detail, paying particular attention to sub-dominant terms in the free energy. These terms control the stability of individual skyrmions towards shrinking or growing in size. Surprisingly, these sub-dominant terms dramatically change the exponent φN characterizing the decay of energy in the system. We restrict ourselves to dissipative noise-free “model-A” dynamics, ∂t ~ m = −δF/δ~ m, where |~ m| = 1 is maintained as a constraint. Our effective coarse-grained free energy is