Coarsening Dynamics in a Two-dimensional XY model with Hamiltonian Dynamics

TL;DR

This paper studies the coarsening process in a 2D Hamiltonian XY model, revealing superdiffusive growth, defect decay, and unique autocorrelation behavior influenced by angular momentum conservation.

Contribution

It provides the first detailed analysis of coarsening dynamics in a Hamiltonian XY model, highlighting the role of angular momentum conservation in these processes.

Findings

Superdiffusive growth of characteristic length scale with 1/z > 1/2

Defect number decreases with exponents 1.0 to 1.1

Potential energy decays with exponent ~0.88

Abstract

We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the kinetic energy and a decrease in the potential energy, with the total energy being conserved. We find that the coarsening dynamics exhibits a consistently superdiffusive growth of a characteristic length scale with 1/z > 1/2 (ranging from 0.54 to 0.57). Also, the number of point defects (vortices and antivortices) decreases with exponents ranging between 1.0 and 1.1. On the other hand, the excess potential energy decays with a typical exponent of 0.88, which shows deviations from the energy-scaling relation. The spin autocorrelation function exhibits a peculiar time dependence with non-power law behavior that can be fitted well by an exponential of logarithmic power in time. We argue that the conservation of the total Josephson (angular) momentum plays a crucial role for these novel features of coarsening in the Hamiltonian XY model.