Local and global persistence exponents of two quenched continuous lattice spin models

TL;DR

This paper estimates local and global persistence exponents in quenched two-dimensional XY and three-dimensional Heisenberg models using numerical simulations, confirming temperature universality and analyzing correlated persistence sites.

Contribution

It introduces a method to simultaneously estimate local and global persistence exponents and investigates their temperature universality and scaling in phase ordering.

Findings

Global and local persistence exponents are estimated for XY and Heisenberg models.

Temperature universality of exponents is confirmed for the 3D Heisenberg model.

Scaling of correlated persistence sites behaves similarly to phase ordering length scales.

Abstract

Local and global persistence exponents associated with zero temperature quenched dynamics of two dimensional XY model and three dimensional Heisenberg model have been estimated using numerical simulations. We have used the method of block persistence to find both global and local exponents simultaneously (in a single simulation). Temperature universality of both the exponents for three dimensional Heisenberg model has been confirmed by simulating the stochastic (with noise) version of the equation of motion. The noise amplitudes added were small enough to retain the dynamics below criticality. In the second part of our work we have studied scaling associated with correlated persistence sites in the three dimensional Heisenberg model in the later stages of the dynamics. The relevant length scale associated with correlated persistent sites was found to behave in a manner similar to the dynamic length scale associated with the phase ordering dynamics.