Differences in the scaling laws of canonical and microcanonical coarsening dynamics for long-range interacting systems

Abstract

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 ${\varphi }^4$ 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.

References in corpus (5)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Geometric properties of two-dimensional coarsening with weak disorder
• One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes
• Vlasov equation for long-range interactions on a lattice
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling

Cited by in corpus (2)

• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain