Differences in the scaling laws of canonical and microcanonical coarsening dynamics for long-range interacting systems
Résumé
We investigate the effects of Hamiltonian and Langevin microscopic dynamics on the growth laws of domains in coarsening. Using a one-dimensional class of generalized φ 4 models with power-law decaying interactions, we show that the two dynamics exhibit scaling regimes characterized by different scaling laws for the coarsening dynamics. For Langevin dynamics, it concurs with the exponent of defect dynamics, while Hamiltonian dynamics reveals new scaling laws with distinct early-time and a late-time regimes. This new behaviour can be understood as an effect of energy conservation, which induces a coupling between the dynamics of the local temperature field and of the order parameter, eventually resulting in smooth interfaces between the domains. Introduction.-If an Ising model is quenched from a high temperature disordered equilibrium state to temperatures below the critical one, coarsening takes place [1]. Coarsening manifests itself by the emergence of ordered ferromagnetic domains, and the subsequent scale-free growth of the larger domains at the expense of the smaller ones [2]. This phenomenon has been mostly studied for models with nearest neighbour interactions [1] in absence or presence of disorder [3]. The theory is based on the hypothesis that two point spatial correlations are time invariant , provided that the distances are renormalized with a time-dependent length L(t) which usually, at leading order, scales as t 1/z. This scaling hypothesis has been rigorously demonstrated for one-dimensional models [4, 5] and for the Ginzburg-Landau model in the limit of infinite components of the order parameter [6]. However, simulations and experiments indicate its wider applicability [1, 2, 7]. Most of the studies were carried out within the canonical ensemble. Nonetheless, some authors [8-11] have performed simulations of the two-dimensional φ 4 model with nearest-neighbour couplings in the micro-canonical ensemble, verifying the scaling hypothesis but without finding agreement on whether the scaling expo
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