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

## TL;DR

This paper compares how Hamiltonian and Langevin dynamics influence domain growth in long-range interacting systems, revealing distinct scaling laws and the impact of energy conservation on coarsening behavior.

## Contribution

It demonstrates that Hamiltonian and Langevin dynamics lead to different coarsening scaling laws in long-range systems, highlighting the role of energy conservation.

## Key findings

- Langevin dynamics aligns with defect dynamics exponents.
- Hamiltonian dynamics shows unique early and late-time scaling laws.
- Energy conservation couples temperature and order parameter dynamics.

## 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 $\phi^4$ 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.